

















Class_■ ~ ' : 

Book __ lA _ 'L. 


GopightN?. 


\« \ 


COPYRIGHT DEPOSIT. 








SHOP 

PROBLEMS 



Third Edition 
Copyright 1913 

ijtJk 

R. J. WATSON 


5 

J 

) > 
> ) ) 


PUBLISHED BY CASINO TECHNICAL NIGHT SCHOOL 
EAST PITTSBURGH, PA. 

Price $1.00 










DEC 30 1913 



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circumference 



LINES 


VERTICAL 



PARALLEL 



6 


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PERPEN- O 
DICULAR i 
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CURVED LINES 



P °^ T A POINT DENOTES POSITION ONLY-NO DIMENSIONS 
































































































































3 


PREFACE 


T HIS collection of problems is intended to supplement 
the standard text books in Arithmetic, providing 
numerous examples of the practical application of 
Arithmetical principles to the things of every day life. Ow¬ 
ing to the location of the Casino Technical Night School 
these problems deal largely with materials common to 
manufacturing industries. No sharp lines have been drawn 
between the ordinary divisions of Arithmetic, such as frac¬ 
tions, decimals, percentage, proportion, etc. This has been 
done in order that the student may avoid any tendency to 
memorize stated forms and rules without first receiving a 
clear interpretation of the processes involved. 

While the principles of Arithmetic are fundamental 
and essential to every student, the application of these prin¬ 
ciples is of far greater importance. A clear comprehension 
of the various operations and what they mean can come 
only through repeated application. 

The attention of the student has been focused on the 
meaning of the problem and not on the memorizing of 
methods of solution. 

The need of a principle is the true reason for teaching 
it and a full understanding of the principle on the part of 
the pupil enables him to formulate the rule in his own 
language, and to apply it to his needs. 

The problems have been taken in general from actual 
business experiences. The interest manifested by students 
on encountering problems that are real and tangible and 
that concern their daily work, furnishes a natural incentive 
for the solution of the problem. This more readily fixes in 
the student’s mind the principles and rules which are usually 



4 


spoken of as the foundation of Arithmetic. In this manner 
the student finds that the fundamental principles are valu¬ 
able to him as tools and not as attainments in themselves. 
Working for the answer has been discouraged. The mere 
mechanical solution of a problem is valueless. It is only 
when the student can see, think, and act for himself, that 
he is learning profitably. 

Perfection is not claimed for this little edition. Quite 
a number of problems are stated incorrectly or solve to re¬ 
sults not practical. In others, more data than is required 
or less than is sufficient, has been given. These have been 
purposely inserted to arouse deep analytical thought. An 
effort is made to have all problems solved by analysis rather 
than by the application of memorized rules. 

The author wishes to express his appreciation for the 
helpful suggestions of Messrs. C. R. Dooley, G. H. F. Holy, 
O. C. Edwards, W. G. Horn, W. J. Kaup and Graham 
Bright. Suggestions for further improvement, or errors 
noted, will be gladly received. 

R. J. WATSON. 



SHOP PROBLEMS 


5 


A FEW SHORT SUGGESTIONS. 

TRIANGLES. The area of a triangle equals % of the 
product of the base and altitude; or, when only the three 
sides of the triangle are known;—from x /2 the sum of the 
three sides, subtract each side separately. Multiply the half 
sum and the three remainders together. The square root 
of this product is the area. 

A triangle has three altitudes, three medians and three 
bisectors. The altitude is the perpendicular distance from 
the base to the apex of the triangle. Any side of a triangle 
may be used as a base. The altitude on any side of a tri¬ 
angle is found by dividing the area of the triangle by one- 
half the legnth of that side. The median is a line drawn 
from the apex of a triangle to the middle of the opposite side. 
The bisector is a line drawn to the opposite side from the 
apex of any angle of the triangle and bisects the angle from 
which it is drawn. The three medians of a triangle meet 
at a common point which is the center of gravity of a body 
of uniform thickness. The three bisectors of the angles of 
a triangle meet at a common point, which is the center of 
the inscribed circle. These three points are not identical 
except in an equilateral triangle. The sum of the angles of 
any triangle is equal to 180 degrees or two right angles. 

RECTANGLE-RHOMBUS AND RHOMBOID. The area 
equals the base times the altitude. 

TRAPEZOID. The area equals one-half the sum of the 
parallel sides times the altitude. 

CIRCLE. The circumference equals the diameter times 
3.1416. The area equals the radius squared times 3.1416. 
To find the area of a circular ring formed by two concentric 
circles, square the radius of each circle, subtract and multi¬ 
ply the difference by 3.1416. 

ELLIPSE. The area equals the product of the semi-axes 
times 3.1416. 

Note: The area of similar surfaces are to each other as 
the squares of their like dimensions. Is the converse true? 
State the converse. 



6 


PRISMS AND CYLINDERS. The area of the sides of a 
prism is called the lateral surface. The area of the curved 
surface of a cylinder is called the convex surface. The dis¬ 
tance around the base of a prism is its perimeter. The dis¬ 
tance around the base of a cylinder is its circumference. 

The lateral surface of a prism equals its perimeter times 
its height. 

The convex surface of a cylinder equals its circumference 
times its height. 

The volume of a prism or cylinder equals the area of the 
base times the height. 

PYRAMIDS AND CONES. The area of the convex sur¬ 
face of a cone equals the circumference of its base times 
one-lialf of its slant height. 

The area of the lateral surface of a pyramid equals the 
perimeter of its base times one-half of its slant height. 

To find the entire surface of a pyramid or cone add the 
area of the base to the lateral surface, if a pyramid; or the 
convex surface, if the object is a cone. 

VOLUME OF PYRAMIDS AND CONES. The volume 
equals the area of the base times one-third the altitude. 

Note: The volume of a prism is equal to 3 pyramids 
having a base and altitude equal to the given pyramid. 

SPHERE. The surface of a sphere equals the circum¬ 
ference times the diameter, or n times the diameter squared. 

VOLUME OF SPHERE-SPHEROID-FRUSTRUM OF A 
PYRAMID OR FRUSTRUM OF A CONE. The volume 
equals the area of both bases plus four times the area of a 
cross section half way between the two bases, and this sum 
to be multiplied by one-sixtli of the altitude. 

Note: In a sphere and spheroid the bases are zero. Also 
the volume of a sphere equals the diameter cubed times 
.5236. 

A line drawn from the center of a chord to the circum¬ 
ference and perpendicular to the chord is called the per¬ 
pendicular bisector. 

To find the diameter of a circle when the chord and per¬ 
pendicular bisector of the chord are given. One-half of the 
chord squared divided by the perpendicular bisector plus 


7 

the perpendicular bisector equals the diameter of the circle. 
(See Wentworth’s Plane Geometry Book III Theorem XV 
1J337, Article I.) 

Table giving the length of a side of a polygon of from 
3 to 100 sides for a circle of unit diameter. 


N 

S 

N 

S 

N 

S 

N 

S 

1 


26 

.12054 

51 

.061561 

76 

.041325 

2 


27 

.11609 

52 

.060378 

77 

.040789 

3 

.86603 

28 

.11197 

53 

.059241 

78 

.040266 

4 

.70711 

29 

.10812 

54 

.058145 

79 

.039757 

5 

.58779 

30 

.10453 

55 

.057089 

80 

.039260 

6 

.50000 

31 

.10117 

56 

.056070 

81 

.038775 

7 

.43388 

32 

.098017 

57 

.055088 

82 

.038303 

8 

.38268 

33 

.095056 

58 

.054139 

83 

.037841 

9 

.34202 

34 

.092268 

59 

.053222 

84 

.037391 

10 

.30902 

35, 

-.089639 

60 

.052336 

85 

.036952 

11 

.28173 

36 

\087156 

61 

.051479 

86 

.036522 

12 

.25882 

37 

384806 

62 

.050649 

87 

.036102 

13 

.23932 

38 

.082579 

63 

.049846 

88 

.035692 

14 

.22252 

39 

.080466 

64 

.049068 

89 

.035291 

15 

.20791 

40 

.078459 

65 

.048313 

90 

.034899 

16 

.19509 

41 

.076549 

66 

.047582 

91 

.034516 

17 

.18375 

42 

.074730 

67 

.046872 

92 

.034141 

18 

.17365 

43 

.072995 

68 

.046183 

93 

.033774 

19 

.16460 

44 

.071339 

69 

.045515 

94 

.033415 

20 

.15643 

45 

.069757 

70 

.044865 

95 

.033063 

21 

.14904 

46 

.068243 

71 

.044233 

96 

.032719 

22 

.14232 

47 

.066793 

72 

.043619 

97 

.032382 

23 

.13617 

48 

.065403 

73 

.043022 

98 

.032052 

24 

.13053 

49 

.064070 

74 

.042441 

99 

.031728 

25 

.12533 

50 

.062791 

75 

.041876 

100 

.031411 


Note: To find the length of a side of a polygon in a circle 
of any diameter, find the number of sides required in a 
column headed “N,” and then multiply the number in 
column headed “S” by the diameter desired. Result is 
length of chord. 

Example—What is the length of a side of a polygon of 
19 sides inscribed in a 12-inch circle? 

Under “N” find 19, and opposite 19 find .16460. 

12 times .16460 = 1.97520 inches. Ans. 


8 


METRIC MEASURE. 


The Metric System is a system of weights and measures 
based on the Decimal Scale the same as our United States 
Money Table. When the names of different values are once 
learned the table is simple and easy to use. 

METER. The unit of length is the Meter, equal to 39.37 inches. 
LITER. (led ter). The unit of capacity equal to 1.05668 liquid 
quart or .9081 dry quart. 

GRAM. The unit of weight, equal to 15.4324 gr. or about 15£ grains. 
KILOGRAM, equal to 2.20462 lb. avoirdupois or about 2 1/5 lbs. 


£ „ M 

g D l) 

g,c <u 

rV ~ t-1 


o jrs 
« 


The Prefix 

Means 

As in 

Which Means 

myria. 

....10,000 

myriameters . 

10,000 meters. 

kilo-. 

.... 1,000 

kilograms . 

1,000 grams. 

hekto-. 

. 100 

hektoliter . 

100 liters. 

deka-. 

10 

dekameter . 

10 meters. 


1 meter, liter, or gram 

1 

deci-.. 

0.1 

decimeter . 

0.01 “ “ 

centi-. 

0.01 

centigram . 

0.1 of a meter. 

milli-. 

0.001 millimeter . 

0.001 “ " “ 


LONG MEASURE 


1 myriameter .— 

1 kilometer (km).= 

1 hektometer.— 

1 dekameter .— 

1 Meter .= 

1 decimeter (dm).— 

1 centimeter (cm).— 

1-millimeter (mm).... — 


10,000 meters. 

1,000 “ or .62 of a mile. 

100 
10 

1 meter, or 39.37 inches. 
0.1 of a meter. 

0.01 “ “ “ 

0.001 “ “ 


MEASURES OF WEIGHT 


1 metric ton (t).= 1,000,000 grams. 

1 quintal (q).= 100,000 “ 

1 myriagram.= 10,000 “ 

1 kilogram (kg). — 1,000 “ or 21/5 lbs. 

1 hektogram .= 100 “ 

1 dekagram .= 10 “ 

GRAM (g). 1 “ or 15 1/2 gr. 

1 decigram.= 0.1 of a gram. 

1 centigram (eg).= 0.01 “ “ “ 

1 milligram (mg).= 0.001 “ “ “ 


MEASURES OF CAPACITY 

1 hektoliter (hi).= 100 liters. 


1 dekaliter .= 10 “ 

1 LITER (1).— l “ or about 1 liquid quart. 

1 deciliter (dl).— 0.1 of a liter. 

1 centiliter (cl).= 0.01 “ “ “ 


1 milliliter (ml).= 0.001 ‘ “ “ 

A liter is a cubic decimeter. In size it is 3.937 inches long, 3.937 inches 
wide, and 3.937 inches deep. It holds about 1 quart, liquid measure. 







































9 


TABLE OF WEIGHTS. 

MATERIALS 


lbs. Per Lbs. Per 
Cu. Ft. Cu. In. 


Alder. 

Aluminum. 

Antimony... 

Apple. 

Ash. 

Asbestos, Pressed 
“ Loose.... 


42 

166.5 

421.6 
47 
45 


.096 

.043 

.033 


Bamboo.... 

Beech. 

Bismuth... 

Birch. 

Box Wood 
Brass— 


22 

46 

612.4 

41 

60.5 


Copper & Zinc. 


80 20 . 

536.3 

70 30. 

523.8 

60 40. 

521.3 

50 60. 

511.4 

Bronze— 


Copper & Tin. 


95 5. 

552 

80 20 . 

552 

Cadmium. 

539 

Cedar. 

39 

Cement, Portland.. 


Cherry. 

41 

Chestnut. 

35 . 

Copper. 

552 

Cork. 

15 

Cypress. 

S3 

Dogwood. 

47 

Kbony. 

76 

Him. 

33 

Fir. 

37 

Fish Paper. 

Glass, Average. 


Gold, Pure. 

1200.9 

G 11 m. 

57 

Gutta Percha. 

Hemlock. 

24 

Hickory. 

48 


.320 


.3195 


.052 


.050 

.100 


.034 



Lbs. Per 
Cu. Ft. 

Holly. . 

47 

Iridium. 

P96 

Iron, Cast. 

450 

Iron, Wrought 

480 

Juniper. 

35 

Larch. 

35 

Lead. 

709.7 

Leather. 


Lignum Vitae. 

62 

Linden. 

37 

Locust. 

46 

Magnesium— 

109 

Mahogany. 

61 

Manganese. 

499 

Maple. 

42 

Marble. 


Mercury, 32°... 

849.3 

“ 60°... 

846.8 

“ 212 °.. 

834.4 

Mica, Sheet. 


Mulberry. 

46 

Nickel . 

548.7 

Oak, Live. 

69 

Oak, White. 

48 

Oak, Red. 

46 

Pine, White ... 

28 

Pine, Yellow... 

38 

Poplar. 

30 

Platinum. 

1347 

Rubber Hard.. 


Rubber Soft... 


Silver. 

655.1 

Spruce . 

28 

Steel. 

489.6 

Sycamore. 

37 

Teak. 

51 

Tin. 

458.3 

Walnut. 

36 

Willow. 

34 

Zinc. 

436.5 


Lbs. Per 
Cu. In. 


.261 

.278 


.411 

.028 


.093 


.105 


.045 

.060 


.283 


7000 gr. — 1 lb. avoir 
5760 gr. = 1 lb. troy. 

LONG MEASURE 

12 in.—1 foot. 

3 ft.—1 yd. 

51/2 yds.—1 rod. 
320 rods—1 mile. 
5280 ft.—1 mile. 


231 cu. in. = 1 gal. 

62| lbs. of water = 1 cu. ft. 

SQUARE MEASURE 

144 sq. in.—1 sq. ft. 

9 sq. ft.—1 sq. yd. 

30^ sq. yds.—1 sq. rd. 
160 sq. rd.—1 acre. 


1 

. •« 

0.015625 

0.03125 

12 3 

, 84 

U.U400/5 

r «" S 

0.00 1 5 

3 « 

O.U/olZ5 

52 7 

o.uyj/o 

0.109375 

0.125 

0 140625 
0.15625 
0.171875 
0.1875 

0 203125 

0.21875 

0.234375 

0 250 

0 265625 
0.28125 

0 2 96875 

0 3125 

0 328125 

0 34375 

0 359375 

0 375 

0 390625 

0 40625 

1 M 

i y 

5 “ 

12 1. 

3 *4 

.3_ 

7 *4 

32 IS 

, 64 

* 1 7 

9 84 

* 2 I* 

5 M 

10 2. 

.1 64 

4 "a- 

1 a- 

32 2 , 

7 64 

0 4375 

0 4S3I25 

0 46875 

0 404375 

0 500 

0 515625 

0 53125 
0.546875 

0 5625 

0 578125 

0 59375 

0 609375 

0 625 

0 640625 

0 65625 

0 671875 

0 6875 

A TIHriOK 

i6 3* 

.5 * 4 

52 31 

1 $4 

2 33 

17 64 

52 3$ 

9 ?4 

16 37 

,j 64 

2 "a- 

a 41 

21 

32 43 

a « 4 

'• 45 

23 64 

0 71875 

0 734375 

0 750 

0 765625 

0 78125 

0 796875 

0 0125 

0 828125 
0.84375 

0 859375 

0 875 

0 890625 

0 90625 

0 921875 
0.9375 

0 953125 

0 95675 

0 984575 

32 47 

3 « 4 

4 4*_ 

25 64 

32 5. 

< ,3 44 

< 16 S3 

in 22 ‘ 4 

n 32 „ 

P. 7 S*~ 

9 6 37 

F H ** 

32 sa_ 

O 13 64 

• ' 6 ji 


32 63 

«4 


CIRCULAR MEASURE 

60 seconds—1 minute. 30 degrees—1 sign. 

60 minutes—1 degree. 90 degrees—1 quadrant. 

4 quadrants, 360 degrees, 1 circle. 
























































































































































10 


HIGH SPEED UPRIGHT DRILL PRESS 
The Cincinnati Rickford Tool Co. 
Cincinnati, Ohio 


1. Spindle driving bevel gears. 

2. Spindle reversing clutch. 

3. Reversing clutch lever. 

4. Back gears. 

5. Back gear clutch. 

6. Back gear clutch fork. 

7. Back gear lever. 

8. Top driving shaft miters. 

9. Vertical driving shaft. 

10. Lower driving bevels. 

11. Speed box. 

12. Speed box tumbler plate. 

13. Speed box back gear lever. 

14. Tool tray. 

15. Tight and loose pulleys. 

16. Belt shifting fingers. 

17. Base. 

18. Column. 

19. Back brace. 

20. Top yoke. 

21. Tapping attachment bracket. 


22. Table arm. 

23. Table arm clamping lever. 

24. Table. 

25. Table clamping lever. 

26. Sliding head. 

27. Head adjusting wrench. 

28. Spindle. 

29. Spindle sleeve. 

30. Ball thrust bearing. 

31. Trip collar. 

32. Counterweight chain. 

33. Trip lever. 

34. Worm box lever. 

35. Quick return lever. 

36. Main feed gear. 

37. Feed box. 

38. Feed change handle. 

39. Feed shaft. 

40. Feed bevel gear. 

41. Feed rack pinion. 

42. Feed hand wheel. 



HIGH SPEED UPRIGHT DRILL PRESS. 


The Cincinnati Bickford Tool Company - Cincinnati, Ohio 


10 A 














11 


Miscellaneous Problems 

1. A bar of steel is 6" thick, 8" wide and 3' long. 

Estimate the weight of the above bar, set down your 
estimate and then find its exact weight. How many pounds 
difference between your estimate and the exact weight of 
the bar? 

2. One cu. ft. of aluminum weighs 165.5 lbs. and a cu. 
ft. of steel weighs 489.6 lbs. We have 2 sheets of metal, one 
of alumiuum and the other of steel. Each sheet is *4" 
thick, 18" wide and 6' long. What is the weight of each 
sheet of metal? 

3. What is the average weight of the following cast¬ 
ings: first, 27.75 lbs.; second, 427.7 lbs.; third, 892.875 lbs.; 
fourth, 1987 lbs.; fifth, 1 ton 355 lbs.? 

4. The Crane Department drew from the store-room 
a barrel of lubricating oil containing 51.5 gallons. After 
using 4.75 gal., how many gallons were left in the barrel? 

5. The following pieces of scrap bar steel %" in diam¬ 
eter weigh respectively 3.75 lbs., 8.5 lbs., 13.25 lbs., 26.875 
lbs., 33.75 lbs., 47.2 lbs. If they are welded into one bar and 
then cut into 5 equal lengths, what will be the weight of 
each length? 

6. How much space will be occupied by seven No. 10 
single cotton covered copper wires laid side by side in a 
conduit? Size of single cotton covered No. 10 copper wire 
is 0.107". 

7. What decimal part of a foot is 5"? 

8. What decimal part of a foot is %"? 

9. How many punchings each .0281 of an inch thick 
are required to build an armature 18" long? What is the 
weight of the iron used, if each punching weighs 5Y2 oz.? 

10. What is the value of 1637845 lbs. of pig iron at 
$32.75 per ton? 

11. A coal dealer sold to a firm three (3) shipments of 
coal, as follows: 4235 lbs., 6475 lbs., 8364 lbs., at $4.20 a 
ton, and took in exchange tungsten lamps at $0.50 each. 
How many did he get? 

12. How many times greater is the surface of a bed¬ 
plate 4' by 8' than one 2' by 4' ? 


12 


13. What will it cost to wire 2% miles of double track 
car line with No. 0000 trolley wire; 640 lbs. to 1000', at 
19%^ a lb.? 

14. “A” can machine a motor bracket in 7% minutes, 
“B” can do one in 6 % mniutes, “G” in 6^3 minutes, “D” in 
7 Ys minutes. If they all start at the same time, how long 
will it be before they are all finishing one at the same time? 
How many brackets will each have finished? 

15. There are 10 castings which weigh as follows: 42% 
lbs., 431/4 lbs., 391/2 lbs., 411/2 lbs., 43 lbs., 3734 lbs., 393/4 
lbs., 43% lbs., 42 lbs., 43lbs., 41 lbs. What is the average 
weight? 

16. A tool has a cutting feed of What is the length 

of the shaft if it makes 288 revolutions while the tool travels 
its entire length? 

17. The cost of making a casting is as follows: % of the 
entire cost for the pattern, 1/12 for making core, % for 
moulding, % for machining. What is the cost of each item 
of labor, if the material costs $6.80? 

18. What is the weight of an iron bar 2' long, 4" wide, 
and 3" thick? 

19. A reel of copper wire weighing 235 lbs. contains 
2100' of wire. How many feet are required for an order 
that calls for 30 lbs.? The weight of the empty reel is 60 lbs. 

20. Find the weight of a slab of marble 7' long, 3' wide, 
2" thick. 

21. What will it cost for a single row of poles for 3% 
miles of trolley line, if poles are 120' apart and cost 15^ 
per foot? Use 35' poles. 

22. What is the difference between a 6" cube and 6 cu. 
inches ? 

23. How many 2" cubes can be cut from a block of 
wood 6" wide, 8" long and 4" thick? 

24. How many perch of stone in a wall 20' long, 6' high 
and 3' wide? 

25. What is the weight of six unmounted switchboards 
of Vermont marble, each board 7' long, 3%' wide and 2%" 
thick? 


13 

26. A bed plate six feet long has an area of 24 sq. ft. 
How long will it take to plane across it if the tool takes %" 
cut and consumes 10 sec. in making one cut? 

27. How many times will a shaft 3 long turn in a 
lathe while the tool travels its entire length? Feed *4" 

28. An armature coil weighs 1 lb. 3 oz. and is made of 
No. 10 copper wire. How many such coils can be made 
from a reel of wire weighing 200 lbs.? 

29. The Blacksmith Shop received 25 bars of steel, each 
bar 10' long, 3" wide and IV 2 " thick. How much did they 
weigh ? 

30. How many cubic inches in a steel plate 30" long, 12" 
wide and 2" thick? What does it weigh? 

31. How long will it take to plane a bed plate 4' 6" wide, 
if a finished and roughing cut are taken across it, each cut 
being %" wide and requiring 19 seconds? 

32. How many days of 9% hours each, must a boy work 
to earn $75.00, if his rate is 15^ per hour? 

33. How much sheet iron will be required to line a box 
8 ' long, 6' wide, and 4' high? 

34. Five boys working on bolt machines each complete 
a bolt in the following time: 1st, 3 min.; 2d, 3*4 min.; 3d, 
3% min.; 4th, 3% min.; 5th, 4 min. If the boys each start 
a bolt at the same time, how many bolts will each boy have 
finished if they all work until they finish a bolt at the same 
time? 

35. What is the difference in weight between a wrought 
iron bar 2' by 1" by %" and a steel bar of the same di¬ 
mensions? 

36. A piece of bronze weighing 7% lbs. contains 6 *4 lbs. 
of copper, and the balance is tin. What decimal part of the 
bronze is tin? What decimal part of the bronze is copper? 

37. A man can put the coils on 3 machines in 14 hours. 
With the help of an apprentice he can do the work in 10 
hours. How long would it take the apprentice to do the 
work alone? 

38. The distance from center to center of adjacent slots 
on a punching is 0.812 of an inch on the circumference. 
How many slots are there in a punching whose circumfer¬ 
ence is 58,464 inches? 


14 


39. A cubic foot of a certain grade of brass weighs 523.8 
lbs. How many cubic inches are there in a brass casting of 
the same grade that weighs 45 lbs. ? 

40. If it takes 3 oz. of solder to fasten the wire in 4 ter¬ 
minals, how many ounces will be required for 15 terminals? 

41. What is the cost of soldering the 15 terminals, if it 
took a man, rated at 27^ an hour, 1% hours, and the solder 
cost $4.29 a cwt.? See No. 40. 

42. The entire length of a holt is 3.75 inches, the head is 
0.625 of an inch long, the body is threaded 2 /z of its length. 
How many threads has the bolt, if the pitch is 0.125 of an 
inch? Draw sketch. 

43. “A” can do a piece of work in 6 days, “B” in 7 days 
and “G” in 9 days. How many days will it take the three 
working together? 

44. The wheels on a traveling crane are 26" in diameter. 
How many turns will one of the wheels make in going a 
distance of 500'? 

45. If the circumference of an oil ring is 20".42, what is 
its diameter? 

46. The wheels on a traveling crane are 28 1 /2" in diam¬ 
eter. Find the number of times the wheels turn in going a 
distance of 300 feet. 

47. What is the weight of a steel plate 18"xl6"x2"? 

48. The driving wheels of a locomotive have a circum¬ 
ference of 20'.42. How many revolutions per minute must 
each wheel make to travel 40 miles an hour? 

49. How many punchings each .0281 of an inch thick 
are required to build an armature 21" long? What is the 
weight of the iron used, if each punching weighs 614 oz.? 

50. A tank 5'x4'x3' is ^ full of oil. How many barrels 
of 53V2 gallons each are in tank? 

51. The dimensions of the base of a tank that will hold 
140 gallons are 3' 5" x 2' 7". How deep is it? 

52. What is the difference between two bars, one of 
steel, the other of cast iron? Each bar is 9%' long, S 1 /^" 
wide and 3%" thick. 


15 

53. How much lumber will be required to build a box 
for shipping a motor, if the over-all dimensions are lO 1 /^' 
by 8%' by 7'. What kind and what thickness of lumber 
would you use? 

54. The above motor is to be crated for sea shipment, 
which requires the box to be lined with tin. How many 
square feet of tin are needed? 

55. A piece of copper 4' long by 2"x2" is to be drawn 
out into a strip *4" wide by ^4" thick. How long will the 
strip be? 

56. A bar of steel 3" wide and 3' long weighs 61.128 
lbs. How thick is it? 

57. How many coils, each containing 375'-6" of wire can 
be wound from a reel containing 1,800' of copper wire? 
What is the weight of the wire on the reel if 100' weighs 
4.75 lbs.? 

58. The distance measured on the circumference of a 
commutator from the center of one bar to the center of the 
adjacent bar is 0".2992. How many bars has the commu¬ 
tator if its diameter is 8" ? 

59. If the electrical conditions in the above problem 
were such that 5 additional bars were required, what is the 
distance between centers of adjacent bars? 

60. How many sheets of mica insulation will be needed 
to insulate 540 bars for the stationary part of an A. C. ma¬ 
chine? Each bar is 42" long, 2" wide, 1" thick and insu¬ 
lated to within 3" of the ends with a double thickness of 
mica. Size of mica sheets 36" by 18". 

61. What is the maximum allowable speed to drive a 
cast iron pulley 28" in diameter, if 5000' per minute is the 
safe allowable peripheral speed for cast iron? 

62. An emery wheel when new is 12" in diameter and 
runs at 1200 r.p.m. After operating for 4 months, its diam¬ 
eter is reduced to 9". How much has its peripheral speed 
been reduced, the speed of the line shaft being constant? 

63. What is the area in square feet of the faces of a cube 
having a 9" edge? 

64. A piece of work in a lathe is making 180 r.p.m. If 
the cutting edge of the tool is 8" from the lathe center, at 
what rate in feet per minute is the metal being cut by the 
tool? 


16 


FULL UNIVERSAL RADIAL DRILL PRESS 


The Cincinnati Bickford Tool Co. 


Cincinnati, Ohio 


1 . 

Vertical driving shaft gear. 

28. 

Driving pulley. 

2. 

Center driving shaft gear. 

29. 

Speed box. 

3. 

Elevating screw gear. 

30. 

Speed box tumbler plate. 

4. 

Elevating Tumbler plate. 

31. 

Speed plate. 

5. 

Tumbler plate segment. 

32. 

Tool tray. 

6. 

Column cap. 

33. 

Box table. 

7. 

Cap gear guard. 

34. 

Base. 

8. 

Vertical driving shaft. 

35. 

Spindle. 

9. 

Elevating screw. 

36. 

Spindle sleeve. 

10. 

Elevating shaft. 

37. 

Feed rack. 

11. 

Elevating lever. 

38. 

Feed rack worm shaft. 

12 . 

Arm 

limit stop. 

39. 

Feed worm wheel. 

13. 

Stop 

studs. 

40. 

Feed hand wheel. 

14. 

Arm 

binder levers. 

41. 

Quick return lever. 

15. 

Full 

Universal arm. 

42. 

Quick return head. 

16. 

Arm 

girdle. 

43. 

Feed trip lever. 

17. 

Arm 

worm box. 

44. 

Feed change lever. 

18. 

Arm 

clamping bolts. 

45. 

Depth gauge dial. 

19. 

Arm 

dowel pin. 

46. 

Spindle counterweight. 

20. 

Arm 

miter gear guard. 

47. 

Universal head. 

21. 

Arm 

anti-sag screws. 

48. 

Saddle. 

22. 

Arm 

pointer. 

49. 

Saddle moving gear. 

23. 

Arm 

shaft. 

50. 

Saddle moving hand wheel. 

24. 

Arm 

rack. 

51. 

Back gear lever. 

25. 

Column sleeve. 

52. 

Reversing lever. 

26. 

Column. 

53. 

Head swiveling worm shaft. 

27. 

Sleeve clamping lever. 

54. 

Saddle binder lever. 


3 



PULL UNIVERSAL RADIAL DRILL PRESS. 

The Cincinnati Bickford Tool Company • Cincinnati, Ohio, 


16 A 


















. 





























17 

65. A strip 2" wide has been cut off a bar of wrought 
iron 3' long. The strip weighs 60 lbs. How thick is it? 

66. If four men can wind 13 coils in 7 hours, how long 
will it take 6 men to wind 19 such coils? 

67. If the wages of 16 men for 8 days are $256.00, what 
will be the wages of 22 men for 12 days? 

68. If 11 men build 45 brush-holders in 6 days of 10 
hours each, how many men will it take to build 81 brush- 
holders in 12 days of 10 hours? 

69. A block of marble 1 ' long, 3' wide and 2' thick 
weighs 6930 lbs., what will be the weight of a block of mar¬ 
ble 10'x4'x3'? 

70. If a transformer tank 8%' long, 7%' wide, and 16 3 /4' 
deep holds 7948 gallons of oil, how much will a tank hold 
that is 9%' long by 9%' wide by 13%' deep? 

71. Three men complete 120 oil rings. Their work is to 
one another as %, and 5-12. What number did each 
complete? 

72. Sixteen men can build 40 motors in 37% days of 
9% hours each; how many motors can 41 men build in 27 
days of 8 hours each? 

73. If 3 men can wind 12 armatures in 26 working days, 
how many days will be required for 8 men to wind 14 
armatures of the same size and type? 

74. A foreman in the shop received an order for 25 C. C. 
carbon circuit breakers and promised to deliver them in 5 
days. He puts 8 men on the work and finds that 3 men in 
6 days can build 9 circuit breakers. Will the promise be 
kept? How much time was required? 

75. If it takes 4 men 15 days to complete ^ of a motor, 
how long will it take 3 men to finish the motor? 

76. How many pounds of each of the following metals 
are required to make 1500 pounds of bearing metal? The 
alloy is to consist of tin, copper, antimony, and lead, in the 
ratio of 16, 3, 2 and 1. 

77. If 24 mechanics can assemble 310 type “S” motors 
in 12 days of 9% hours, when can an order for 400 such 
machines be promised if 30 mechanics are put on the job? 
Make an allowance of 2 days for shipment, 


18 


78. In assembling a commutator of 128 bars, two men 
are necessary to do the work. If it takes them 3 hours to 
complete one, when can an order for 300 commutators be 
promised, provided 8 men work on the job 13 hours each 
day? 

79. Two men rough turning shafts, have lathes running 
at different speeds—the ratio being as 3 is to 5. If the man 
on the slow speed lathe turns out 30 shafts for a day’s work, 
how many shafts does the other man rough turn in a day? 

80. The diameter of two pulleys belted together are to 
each other as 3 is to 10. What is the relation of their peri¬ 
pheral speeds when running? If the speed of the smaller 
pulley is 1200 r.p.m., what is the speed of the larger pulley? 

81. A furnace grate 4' 3" by 5' 10" consumes 12 lbs. of 
coal per square foot of grate area per hour. How many 
tons of coal will he consumed in 5% days of 9% hours each 
per day? 

82. The finishing operation on 27 motors requires 8 men 
for 3 days of 9% hours. How much overtime will be re¬ 
quired to complete the same operation on 12 motors if 15 
men are put on the job and begin work at 7 a. m. Saturday? 
All work done between 12.15 p. m. Saturday and 7 a. m. 
Monday is overtime, and is paid for at time and half, or l 1 /^ 
times day work rate. 

83. You are requested to wind up on a l 1 /!" mandrel a 
5' spiral (close wound) of non-resistance wire. Thickness 
of wire is 3/32" in diameter. How many feet of wire will 
this coil require? How many feet will be required if the 
mandrel is 1%" in diameter? What is a mandrel? 

84. A foreman promised to complete an order in 14 
days. He put 6 men on the job, and after working 7 days 
he finds they have three-fifths of the order yet to finish. 
How many days longer than the date promised will it take 
to finish it? How many extra men must be put on the job 
to complete the work 2 days earlier than promised? 

85. We have 800 “CCL” motors in stock. If we sell 5% 
of them to one customer, how many motors did the order 
call for? Solve two ways. 

86. A bearing metal is made up of 80% tin, 10% anti¬ 
mony, 5% copper and 5% lead. How many pounds of each 
metal are required to make 2400 lbs, of bearing metal? 
What is bearing metal? 


19 

87. _ If a company manufactures 3600 machines per year, 
and 15% are returned the first year as unsatisfactory, 12% 
the second year, and 8% the third year, how many ma¬ 
chines does the company dispose of in three years? What 
is the per cent, shop efficiency per year? 

88. If a machine is bought for $625.00 and repairing to 
the amount of $87.00 is expended on it, and then sold at a 
profit of 5%, what was the selling price? 

89. The armature of a railway motor weighs 2400 lbs., 
which is 42% of the total weight of the whole machine, what 
is the weight of the complete motor? What is an arma¬ 
ture? 

90. A reel contains 2480 feet of wire—45% of it is used 
on one stock order, 20% is used on another stock order, and 
55% of what remains is used on a third stock order; the re¬ 
mainder is used on a fourth stock order. How many feet 
are used on each stock order? 

91. If one man in the factory draws $32.50 on pay day 
and a second man’s pay is 10% more than the first, and a 
third man’s pay is 10% more than the second, what is the 
total pay of the three men? 

92. If 10 men can finish 18 machines in 4 days of 9 % 
hours each, how long will it take 8 men, working 10 hours 
per day, to finish 11 1/9% more machines? 

93. Section “W-4” in two weeks grinds 950 tools for the 
factory, 40% are sent to Section “A,” Section “T” receives 
50% as many as Section “A,” Section “B” receives 60% of 
what is then left, and Section “D” the balance. How many 
tools went to each of the above named sections? 

94. Section “F” made 1500 brush-holders, 3% were 
found to be defective, 75% were applied on orders in the 
shop and the balance placed in stock. How many were de¬ 
fective? How many were placed in stock? 

95. What is the selling price of the following motors 
if the first costs $600.00, and is sold at a profit of 12%, 
second costs $850.00 and the profit is 13%%, third costs 
$1275.00, and the profit is 14%%? 

96. A motor is sent to the factory for repairs. The labor 
on the repairs amounts to $75.00; 20% of this amount 
equals the cost of the material. What is the customer’s bill 
if the company makes a profit of 8%% on the above order? 



20 


97. A transformer tank 3'x3%'x6' high is 2 /z full of 
oil. If 17%% of this quantity is taken out, how many gal¬ 
lons of oil are lost? 

98. A casting weighing 325 lbs. was reduced 7% in ma¬ 
chining. What is the weight of the finished casting? How 
many cubic inches of metal were removed? 

99. If in a lot of 5600 bolts, 448 are found to be de¬ 
fective, what is the loss in per cent.? 

100. If the W. E. & M. Co. shipped 2600 fan motors to 
Chicago and 455 were damaged in transportation, what per 
cent, was delivered in good condition? 

101. If 5 men can finish 15 machines in 4 days of 9% 
hours each, how long will it take 4 men working 10 hours 
per day to finish 33per cent, more machines? 

102. If 10 men working on an order which is promised 
in 30 days, finished 33^ per cent, of it in 15 days, and then 
8 additional men are put on, will the promise be kept? If 
the day’s length is 9% hours, how much overtime is re¬ 
quired to keep the promise? 

103. A workman testing coils for short circuit rejected 
15 out of 450 coils. What per cent, was found defective? 

104. On an order calling for 1290 bolts, 1000 have been 
delivered. What per cent, of the order has been completed? 
In the above delivery, 40 bolts were found to be defective. 
What per cent, of the order remained to be filled? 

105. The Company sold 60 fan motors for $12 each and 
gained 10% on half of them and lost 10% on the remainder. 
Did they gain or lose on the whole order, and how much? 

106. The cost of a motor generator set is $5400. If 
this machine was bought for a price 10% less than the cost, 
to which was added $1000 for improvements and then re¬ 
sold at a net profit of 10%, what was the selling price? 

107. A man completed 36 end plates, which is 6% of the 
number ordered. How many end plates were on the order? 

108. A motor is pulling a load of 45 H.P., which is 90% 
of its rating. If the motor can pull a 50% overload, what is 
its maximum horse-power? 

109. An order calls for 750 field coils; 10% of this num¬ 
ber is done by one man, 16% by another, and 46% by a third. 
What per cent, of the work l’emains to be done? 


■HELICAL GEAR DRIVE' 



CAPSTAN” HANDLES ALLOW 
OPERATOR TO MOVE TABLE 
IN BOTH DIRECTIONS FROM 
FRONT OF MACHINE 


VSTANTLY 


FRICTION BRAKE 


POWER FEED CLI T( 
rriMmrvii tjtjt 


QUICK TRAVERSE 


ADJl STABLE AUTOMATIC TRIP 


STOPPING AND STARTING 
lever, also applies 

FRICTION BRAKE 


HAND WORM FEED 

FEED ENGAGEMENT LEVEI 

BALL THRUST BEARING 

LEVER FOR TRIPPING 
AL'TOMATIC FEED BY HAN 


METHOD OF RAISING AND 
LOWERING TABLE AVOIDS 
MAKING HOLE IN FLOOR 


DRILL PRESS. 


Colburn Machine Tool Company - Franklin, Pa. 




20 A 





















. 






































21 

110. Section “A” built 1600 street car motors, 1300 of 
which were shipped to customers, 3% were found to be de¬ 
fective when tested and the balance was placed in stock. 
How many motors were defective? How many were placed 
in stock? 

111. The company sells a motor for $220.00, which is at 
a profit of 10%. What does the motor cost the Company? 

112. A certain order calling for spiders was increased 
44%, making a total of 540 spiders ordered. How many 
spiders were on the original order? What is a spider? 

113. A shaft weighing 348 pounds is 16% heavier than 
a second shaft. What is the weight of the second shaft? 

114. A firm owns 75% of the stock of a subsidiary com¬ 
pany and sells 25% of its holdings for $24,000. What is the 
valuation of the subsidiary company? 

115. A casting weighs % of a lb. rough, and ^ of a lb. 
finished. What per cent, of the original weight is lost in 
machining? Can I gain more than 100%? Illustrate your 
answer. Can I lose more than 100% Explain clearly. 

116. On the basis of averages, we find that a workman 
who loses no time will finish 5400 commutators per year. 
A workman, however, found that his actual work per month 
was as follows: January, 2% increase; February, 3 1 / 4% in¬ 
crease; March, %% loss; April, 2% increase; May, 2 x /2% 
increase; June, 1%% loss; July, l 1 / 2 % increase; August, 1% 
loss; September, 2%% increase; October, 4% increase; No¬ 
vember, %% loss; December, 3% increase. How many 
commutators did he actually finish? 

117. Two salesmen, “A” and “B,” desire to sell a certain 
type of machine to “G”; “A” asked a certain price and “B” 
asked 50% more, claiming higher efficiency for his ma¬ 
chine. “A” then reduced his price 20% and “B” reduced 
his price 30%. At this price “C” bought both machines at 
a total cost of $148.00. What was each man’s original ask¬ 
ing price? 

118. A firm invested $3200.00 in copper wire when it 
was depreciated 40%; what was the actual value of the 
wire? 

119. A purchasing agent working on commission sent 
his firm a bill for $6680.20, stating that $6300.00 were 
for goods purchased, $6.70 for cartage, and $27.00 for 
freight. What rate of commission was he paid? 


22 


120. If a purchasing agent receives a commission of 
3i/ 2 %, what amount will he invest when the firm sends him 
$2846.25? 

121. A section of the new test floor put in the Electric 
Laboratary, is 22^' long by 10' wide. How many square 
feet does it contain? If the new floor had been square, 
what would be the length of one side? 

122. The gable end of a house is 25' wide and 8' 3" high. 
What will it cost to paint both gables at 6 cents per square 
foot? Draw sketch. 

123. What will it cost to paint the two gables of a house 
25' wide and 8' 3" high at 6 cents a square foot? 

124. A lathe is located 6' in front of a line perpendicular 
to the line shaft which is 18' above the floor. If the center 
of the lathe pulley is 3%' above the floor, what is the dis¬ 
tance between centers of the line shaft and the lathe pulley? 

125. If the foot of a ladder 52' long is placed 25' from the 
base of a building, how far must it be drawn out that the 
top may be lowered 4 feet? 

126. What size round stock must be used to make a 
Milling Machine Vise Screw with a 2" square shoulder? 

127. What is the area in square inches of a steel disc 
10" in diameter? 

128. How large a steel disc can be cut from a piece of 
steel 15" square? How many per cent, waste is there? 

129. I have two pieces of steel, each 2" thick and 6" and 
12" square respectively. How do they compare in weight? 

130. How do two steel discs of the same thickness and 
3" and 16" respectively in diameter, compare in weight? 

131. What is the size of the largest square end frame 
that can be put in a Transformer tank whose inside diam¬ 
eter is 32". 

132. What must be the diameter of a transformer tank 
to hold an end frame 3' square? 

133. Allowing 3" on corners for clearance, what must 
he the diameter of a transformer tank that will hold a 40" 
end frame? 


23 

134. How many gallons of oil are needed for a trans¬ 
former 4' in diameter and 6' high, if 45% of the volume is 
taken up by the coils and end frames? 

135. How many square feet of metal will be needed to 
make 25 tanks of the same size as the one in problem No. 
134? 

136. A crane is 28' above the floor. How long a ladder 
will I need to reach the crane if the foot of the ladder is 
placed 10 feet out from the wall and its top rests on the 
crane track? 

137. How long would the ladder need to be in problem 
No. 136, if it was placed on a flat car 4' high? 

138. A tank of inside diameter 8%' x 6^4,' deep x %" 
thick is full of water. What is the entire weight? 

139. A tank x 3^' x 5' is full of oil. How many 

gallons of oil must be taken out if we wish to lower the 
oil level 9"? 

140. If the area of a 9" circle is 63.6174 square inches, 
what is the area of a 10" circle? Of a 4" circle? Of a %" 
circle? Apply law of squares. Note—(Areas of similar 
figures are proportional to the squares of their like dimen¬ 
sions.) 

141. The area of a 7" circle is 38.4846 square inches. 
What is the diameter of one whose area is 49.8256 square 
inches? .0490875 square inches? Apply law of squares. 

142. If a steel shaft weighs 437 lbs., and is 5' 2" long, 
what is its diameter? What would be the weight of one 
whose length was the same, but diameter twice as great? 

143. A pipe IV 2 " in diameter will empty a transformer 
tank in 1 hour. Find the diameter of pipe that will empty 
it in half the time. 

144. A reel of copper wire weighs 210 lbs. net. If it is 
%" in diameter, how long is the wire? 

145. We have a steel test bar which is 8" long and ".508 
in diameter that has been broken. If the elastic limit was 
17800 lbs. and the breaking point was 21300 lbs., what was 
the elastic limit and breaking stress per square inch. What 
is means by elastic limit? 

146. A cubic foot of iron is to be rolled into a sheet %" 
thick. How large a square sheet will it make? 



24 


147. What will be the weight of a steel sector whose 
central angle is 20 degrees? The size of circle from which 
this sector is cut is 4' 9" in diameter and %" thick. 

148. If a cylindrical tank 6' 0" in diameter and 6' 0" 
high is replaced by a tank 4' 0" square, how high should it 
be made? 

149. A telephone company in erecting its line, placed an 
anchor pole at the corner of two roads, one running due 
East and West, the other North and South. A guy wire 75' 
long is attached to this pole 5' from the ground and to a 
50' pole on the West road 5' from its top. A second wire is 
attached to the anchor pole at the same point and connected 
to a 70-foot pole on the South road 5' from its top. The 
second pole is on the South road 80' from the corner. What 
is the length of the wire connecting the tops of the two 
poles? Draw sketches. 

150. The cast iron counter-weight which balances the 
arm on a drill press is a sphere 6" in diameter. What is 
its weight? 

151. The head of a planer is balanced by two counter¬ 
weights, each 6" in diameter and 10" long. The top of each 
weight is hemispherical. What do they weigh? Draw 
sketch of weights. 

152. How much will the weight in problem No. 151 be 
reduced if a 2" hole 7" deep is drilled in each counter¬ 
weight? 

153. We have set up on a horizontal boring mill an In¬ 
duction Motor frame, the finished inside diameter of which 
is to he 18". What is the rate of machining the metal on 
finishing cut if mill is running at 20 r.p.m.? 

154. Find the length of a hand rail for a flight of stairs 
having 30 steps, each step 7 V 2 " high and 9" wide. 

155. What is the weight of a steel shaft 2" in diameter 
and 5' long? 

156. What is the diameter of a steel shaft 4' long that 
weighs 170.7 lbs.? 

157. Two steel shafts each 5' in length and 3" and 6" 
in diameter respectively are lying side by side. Estimate 
the weight of each? Put your estimates on paper and figure 
the exact weight of each shaft. How do your answers com¬ 
pare? 


25 

158. The gas receiver at the end of the works has a 
diameter of 40'. If the bell is 6' lower in the morning than 
in the evening, how many cu. ft. of gas were consumed 
during the night? 

159. A bar of copper 2" in diameter and 5' long is to 
be drawn out into a piece of wire %" in diameter. What 
will be its length? 

160. Over how many square inches of surface will a 
tool travel in making one cut across a shaft 3%" long and 
2 i/ 2 " in diameter? 

161. What is the weight of a cast iron pipe 15' long 
whose outside diameter is 14" and inside diameter is 12"? 

162. Oil is flowing through a 1" pipe at the rate of 30' 
per minute. How many gallons of oil will the same pipe 
discharge in one hour? 

163. How does the weight of a solid cast-iron bar 3" 
in diameter and 6' long compare with the weight of a cast- 
iron bar of the same dimensions that has a 1" hole bored 
through it lengthwise? 

164. How many cu. inches of iron in a piece of standard 
3" pipe, 2' long? The outside diameter of the pipe is 3 Vi"- 
What would this piece weigh? 

165. If a steel shaft 8' 6" long weighs 540 lbs., what size 
of hole should be drilled through it lengthwise to decrease 
its weight 18% ? 

166. What will it cost to paint the sides of a vertical 
boiler 12' high and 65" in diameter at 7 cents a square foot? 

167. What is the number of cubic feet of air that must 
be supplied hourly to a section of the shop 1895' long, 78' 
wide, and 35' high, that the air may be completely changed 
every half hour? 

168. What is the area of a template in the shape of a 
trapezoid ? The length of the parallel sides are 10" and 14" 
respectively and the width or altitude is 8". What is a 
template? 

169. A 1" pipe from a well in the works discharges 1 
gallon of water in 40 seconds. How much should a 2' 
pipe at the same rate of flow discharge in 1 minute? 


26 


170. A tank is being filled with oil from 2 pipes whose 
diameters are 1 and 3"—the rate of flow of oil from 
each pipe is 35 linear feet per minute. In y 2 hour’s time, 
how much more oil is delivered by the 3" pipe than by the 
1 %" pipe? 

Draw sketch of a circle, a circle circumscribed by a 
square, an inscribed square. 

Explain—When do you speak of the circumferance of 
an object? 

When do you speak of the perimeter of an 
object? 

*171. A shaft 3' long whose diameter is 6" is upset on 
one end to make a square shoulder 4" long to fit into a 
bracket with a 6" square hole. How much will the shaft 
he shortened by making this shoulder? What is the area 
of a cross-section of the shaft at its middle? 

*172. In the above problem— 

The other end is hammered out into a shoulder 
4" long to fit a square hole in a bracket. What is the size 
of the shoulder if the corners are in line with the rest of the 
shaft? How much has the shaft been lengthened? Has the 
shaft in above problem been lengthened or shortened by 
these two operations? 

173. How many square feet of tin will he needed to roof 
an oil tank 20' in diameter? The peak of the roof is 6' 
higher than the top of the tank? Add 3% for laps. 

174. How many square feet of tin will he needed to 
make a 10' connection between two heating pipes? The 
diameter of the large pipe is 18" and the diameter of the 
small pipe to be connected is 10". Allow 3% for laps. 

175. What will it cost to make the following scrap ma¬ 
terial, 20 pieces of %" round iron, each 2' 6" long, into 
four bars of equal length, if the blacksmith charges 6 cents 
for each weld and 4 cents for each cut made in doing the 
work ? 

176. What is a prism? Draw sketch. What is the en¬ 
tire surface of a triangular prism whose base measures 5" 
on a side and whose height is 5" ? 

177. What is the number of square inches of surface on 
a figure similar to above problem whose altitude is 7%' and 
one side of base 6'? What is its volume? 


RAPID TRAVERSE FRICTION 



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26 A 


VERTICAL BORING MILL. 

Colburn Machine Tool Company - Franklin. I'a. 






























27 

178. The blacksmith uses a piece of cast-iron for form¬ 
ing rings. Its lower base is 10" in diameter, height 36", 
upper base 1" in diameter. What is its circumference 18" 
above lower base? What does it weigh? 

179. What is the weight of a piece of steel %" thick 
whose sides measure 6", 7".5, and 8" respectively? What 
is the shape of this piece of steel? Draw sketch. 

180. What is the length of the shortest line that can be 
drawn from each angle to the opposite side? See problem 
No. 179. Draw sketch. Do these lines have a common 
point of crossing? 

Note—A straight line is the shortest distance be¬ 
tween two points. 

181. What is the weight of a steel rim 4" wide whose 
outside diameter is 46" and inside diameter is 38"? Draw 
sketch. 

182. We have a sheet steel disc 20" in diameter. What 
is the area of the largest square that can be cut from this 
disc? 

*183. What is the area of an ellipse whose transverse 
axis is 32" and conjugate axis 20"? 

*184. Which weighs the most, a steel disc %" thick 
and 10" in diameter or an elliptical disc %" thick, whose 
axes are 10" and 6" respectively? 

185. A certain make of hemp cable 3" in diameter will 
carry a load of 24 tons; what load will a hemp cable carry 
that is 4" in diameter? 

186. I have two rectangular pieces of sheet copper simi¬ 
lar to each other in shape. The size of the smaller sheet is 
3" x 4". The area of the larger sheet is 192 sq. inches. 
What are the dimensions of the larger sheet? 

187. A bar of iron, square at each end, measures 16" at 
small end and 20" at the large end, when set up on end its 
height measures 40". What is its weight? 

188. The Testing Department ordered a ring covered 
with tinfoil. The dimensions of the ring are: Outside 
diameter, 18"; thickness of ring, 2" in diameter. How 
many square inches of tinfoil were used? 

189. The company had an order for 1200 steel wedges; 
size of wedge as follows: Head, 2" by 3"; length of body, 
10". How many lbs. of metal were used if there was a 
loss of 3% in manufacture? 


28 


190. A steel mill has 4896 lbs. of metal to be made up 
into 10 bars, each bar to be 6' long and 3" wide. What will 
be the thickness of these bars? 

191. A round bar of steel 4" in diameter and 4' long is 
to be made into a shaft with the dimensions as follows: 
4"x3"; 8"x3i/ 4 "; 15"x3y 2 "; 9"x 3%"; 8"x3y 4 "; 4"x3". How 
much metal is scrap? Student will draw sketch. 

192. A piece of sheet iron 5' long is to be corrugated. 
Assuming the corrugations to he semi-circular of 3" pitch, 
what will he the width of the finished plate? 

193. Twenty weights for Mercury Rectifier Outfits are 
sent to “W-l” to he reduced 40 lbs. in weight each. The 
face from which the stock is to he taken is 3' 1%" long and 
3Y2" wide. The ends are curved, having a 1%" radius. 
How deep must the cut he to reduce each to the required 
weight? Draw sketch. 

What is a sector? A segment? What is meant 
by central angle? Draw sketch illustrating each. 

194. A cut %" deep is to be taken off of a cast-iron base 
3%' long by 2%' wide; how many pounds is it reduced? 

195. A 150-H.P. engine is to drive a 100 K.V.A. alter¬ 
nating-current generator. The speed of the engine is 320 
R.P.M. and the speed of the generator is 900 R.P.M. If the 
flywheel of the engine is 45" in diameter what size pulley 
must be used on the generator? 

196. What is the volume of a tank 5' long, 5' wide and 
5' deep? What is the size of a tank similar in shape, but 
holding four times as much? 

197. A tank 3 V 2 ' in diameter and 6' high is to be re¬ 
placed by a cubical tank. What are the dimensions of the 
new tank? 

198. How many times heavier is a sphere 6" in diameter 
than one 2" in diameter. Note—Volume varies as the 
cube of the diameter. 

199. If Yz" round iron weighs 1 lb. to the foot, how 
much ought 2%" round iron weight to the foot? 

200. Which weighs the more, a ball of iron 3" in diam¬ 
eter or three halls 2" in diameter? 

201. A counter-weight 10" in diameter weighs 325 lbs. 
It is desired to keep the same shape for a new one that will 
weigh 450 lbs. What should he its diameter? 



29 

202. How much coal will be needed to run a furnace 
during the month of December? The furnace has a maga¬ 
zine 3' deep and 12" in diameter, which is filled twice daily. 
One cubic foot of the grade of coal used weighs 60 lbs. 

203. The diameters of a prolate spheroid are 24" and 20" 
respectively; what is its volume? 

204. Which has the greater volume, a sphere 12" in 
diameter or a spheroid whose diameters are 16" and 8" 
respectively ? 



205. What will be the weight of a steel hub that is made 
from the above sketch, the dimensions of which are: 
A and A' each 6" in diameter, B and B' each 11" in diam¬ 
eter, C 2' 1" in diameter. F and M each 16" long, G and K 
each 6" long and H 12" long. 

206. If a steel shaft 5" in diameter and 8' long has a 1" 
hole drilled through it (lengthwise) what is the percentage 
of reduction in weight? 

207. A mercury rectifier weight of cast-iron 5%" thick 
has 6 holes 4" deep and 1%" in diameter drilled in it. 
How much is its weight reduced? What per cent, is it 
decreased ? 

208. If you were requested to furnish a plain brass cast¬ 
ing weighing 220 lbs., to be used as a base for a piece of 
apparatus, and you suggested using cast-iron instead of the 
brass, what per cent, of the original cost could be saved by 
following your suggestions? Cast brass costs 15 cents per 
lb. while cast-iron costs 3.2 cents per lb. 































30 



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30 A 


The Cincinnati Planer Company Cincinnati, Ohio. 


















31 


209. What is the area of a regular pen¬ 
tagon, the length of one side of which is 
6 "? AD equals 9".708; BF equals 3".526; 

GD equals 5".706. 

210. Referring to problem No. 209, A 
what is the diameter of the circle that will 
circumscribe the pentagon ? 

211 . Draw a regular pentagon and di¬ 
vide it into five isoscles triangles, using a 
side of the pentagon as the base of the triangle. Referring 
to problem No. 209, what is the area of one of the triangles? 

212 . Referring to problem No. 211, what is the altitude 
of each triangle? 



213. A. B. equals 10", C. V. equals 2". 
What is the length of V. D.? What is the 
diameter of the circle ? 

214. In the above figure, if G. V. equals 
8 " and V. D. equals 50", what is the length 
of A. B.? 

215. If D. V. equals 25" and A. Y. 
equals 10", what is the length of C. V.? 


c 



216. E. F. equals 30", G. H. equals 
25"; what is the diameter of the circle? 
What is the radius and area of the circle? 

If F. G. equals 25", G. H. equals 60"; 
what is the diameter of the circle ? 

217. C. D. equals 30", F. G. equals 5"; 
what is the diameter of the circle? What 
is the radius and area of the circle? 

218. What is the area of a circle of 
which the figure in problem No. 217 repre¬ 
sents a segment? G. F. equals 8", D. F. 
equals 20". 

219. What is the diameter and area of 
a circle with a chord R.S. 20" long and its 
perpendicular bisector T.U. 4" in length? 

220. If U.S. equals 5" and U.T. equals 
2", what is the area of a 90° sector of this 
circle? 
















32 


221. The foreman gave an apprentice a 
segment of a punching used on the field 
of a motor, and asked him to find the di¬ 
ameter of the machine on which it was 
used. The punching measured 32" on its 
chord and the perpendicular distance from 
tlie center of the chord to the circumfer¬ 
ence measured 2".5. What was the diam¬ 
eter? 

222 . The diameter of the circle is 20"; 

K. L. equals 12". What is the distance 
from M to the center of the circle? 

223. In a figure similar to the one 
above, the distance from M to the center 
of the circle is 16" and K. M. equals 12". 

What is the distance from M to the cir¬ 
cumference of the circle? 

224. A broken pulley-wheel was sent to the shop with 
an order for a new pulley of the same size and type. By 
using a straight edge, a chord of 18" was laid off and the 
highest point of the curve was measured from this chord 
and found to be 3". What was the diameter of the pulley? 

What is the ditference between peripheral speed and 
linear speed? What is meant by r.p.m.? What is the safe 
peripheral speed in feet per minute for a cast-iron pulley; 
for an emery wheel; for a grindstone; for a cloth buffing 
wheel? How do you find the r.p.m. of a pulley when you 
know the peripheral speed ? What is liable to happen if the 
safe peripheral speed is exceeded? 

What are machine keys? Draw sketch. What are 
feather keys? Draw sketch and tell how they differ in use 
from machine keys. What is a journal bearing? What is 
a ball bearing? Name some machine having each kind of 
bearing? What is meant by lubricant? Name the differ¬ 
ent kinds of lubricant used in a machine shop. Tell where 
and why each lubricant is used. 











33 



MN equals 40",and passes through the point O. 
RO equals 15". 

OP equals 10". 

MN is perpendicular to AB, CD, and NT; also LK, 
GH, OE and OF are perpendicular to the lines 
to which they are drawn. 

Angle KTN equals 45 degrees. 

From the data and figure solve the following problems: 


225. 

Find 

the ] 

length 

of 

AB. 

226. 

a 

a 

<( 

a 

DC. 

227. 

a 

a 

a 

a 

BC. 

228. 

a 

a 

a 

a 

AC. 

229. 

a 

a 

a 

a 

AN. 

230. 

a 

a 

a 

a 

GH. 

231. 

a 

a 

a 

a 

OE. 

232. 

a 

a 

a 

a 

OF. 

233. 

ii 

u 

a 

a 

MT. 

234. 

a 

a 

a 

a 

LK. 

235. 

a 

a 

a 

a 

LT. 

236. 

Find 

the 

area 

of 

AECO. 

237. 

a 

(6 

a 

a 

AFNO. 

238. 

it 

it 

a 

a 

MKB. 

239. 

if 

ii 

a 

a 

MTL. 

240. 

ii 

it 

a 

a 

MTN. 

241. 

ii 

ii 

a 

a 

MKCN. 

242. 

ii 

ii 

a 

a 

KTNC. 

243. 

a 

ii 

a 

a 

MRS. 

Find the altitude 

of an 

isosceles tri 


in area to the above figure AMLTNDH and having a base 


of 50". 







34 


BELTING AND GEARING. 


Belts and gears are used to transmit power generally 
with change in speed. The speed is generally given in revo¬ 
lutions per minute, (r.p.m.). 



A pulley is driven by a belt by means of friction between 
the surfaces in contact. If no slipping occurs, the peri¬ 
pheral speeds of two pulleys belted together are equal. 

The point of contact of two meshing gears is the pitch 
point. A circle drawn through this point, with the center 
of the gear as its center is the pitch circle. The distance 
measured on this circle (part of the circumference) from 
the center of one tooth to the center of the adjacent tooth 
is called the Circular Pitch, abbreviated C. P. 

The diameter of the pitch circle is called the Pitch 
Diameter, abbreviated P. D. The number of teeth for every 
inch of pitch diameter is called the Diametral Pitch, ab¬ 
breviated D. P. 

Note that D. P. is an abstract number, while C. P. and 
P. D. are usually expressed in inches. 

The Addendum of a gear is the distance from the pitch 

circle to the outer extremity of the tooth and equals 

« 

The Dedemdum of a gear is measured from the pitch 
circle to the clearance circle and is equal to the addendum. 

The clearance is usually taken as —of the thickness of a 

10 

tooth measured on the pitch circle. If “t” represents this 

thickness, then the clearance = — 

10 



















35 



It is a general property of two gears in mesh that their 
pitch diameters are proportional to the number of teeth in 
the gears, and vice versa. 

If the teeth are properly shaped the linear velocities of 
the two gears are equal, and the angular velocities (speeds 
of rotation) are inversely proportional to the number of 
teeth and to the pitch diameters. 

x = 3.1416. Outside diameter of gear = O. D. 

From the above data the following formulae are deduced: 

P. D. X D. P. - Number of teeth or N. 

D. P. X G. P. = x, or D. P. - -— , or G. P. -- 

N + 2 

0. D. =- 

D. P. 

V = velocity of gear or large pulley. 

v = velocity of pinion or small pulley. 

D = diameter of gear or large pulley. 

d = diameter of pinion or small pulley. 

S = speed in r.p.m. of gear or large pulley. 

s = speed in r.p.m. of pinion or small pulley. 
















36 


Then V = it X D X S, and v = x X d X s. 

V x X D X S v DXS 

— =-, or — =- 

v xXdXs v d X s 

.*. V — v, and D X S = d X s 


D = ?t>LL,s = 


d X s d _ D X S 
D ’ s 


S — 


DXS 


From the above data and formulae any of the following 
problems can be readily solved. 



x ►> 

V dt 

s' 

s £ 



4/ 4 J 

H ~ 

* s 

H 3 

. (U 

k a 

O, % 



o 5 

4. Oh 

. ? 
a> Oh 
. 

. Oh 

2 



U o t 

41 O 

u o O 

V 

r\ 

c°o 

3 ° ° 



S 8 

£ ° 
fi o 

u 

TJ rt 

V <u 

7 .2 
y c 

T3 


.2 O 

ca .2 
•2 Oh 

s. ° 

4 J .Z 

a ^ 

a 

245. 

Q 

22% in. - - 

. 2 1-16 in_ 

_ _195 

tn 

s 

246. 

32 in. ___ 

. 4 in. 


1600 

___s 

247. 

3 ft. 8 in. 


400_ 

._1900__ 

_ d 

248. 


12 in. __ 

277 . 

_750_ 

_D 

249. 


15 tep.th 

285 

1290 

G 

250. 

57 teeth i 


530_ . 

_975_ 

P 

251. 

23 in_ 

5 in. 


_400_ 

__S 

252. 

29 in_ 

_ 24 in_ 

_1450 


s 

253. 


17 in. 

_87_ 

. 409__ 

_D 

254. 

20.4 in_ 

. 6.125 in. _ 


_ 79__ 

___S 

255. 

15.4 in. 


_ 214 

. 514 

d 

256. 

64 teeth 

25 teeth 

590 


s 

257. 


19 teeth 

208 

690 

G 

258. 

A gear has 

75 teeth and 

is 3 pitch. 

Find its pitch 


259. How many teeth will be in a pinion to mesh with 
above gear, if its pitch diameter is 4"? 

260. If a pinion of 4" pitch diameter makes 1500 r.p.m. 
find the linear speed at its pitch circle? 

261. A 480 r.p.m. motor is to drive a lathe at 136 r.p.m. 
If a 17 tooth 3 pitch pinion is used, what will be the distance 
between gear centers? 

















































37 

262. A line shaft running at 125 r.p.m. carries five 16" 
pulleys. Find the size of pulley on each of the following 
machines to be driven at speeds of (a) 500 r.p.m., (b) 1200 
r.p.m., (c) 700 r.p.m., (d) 375 r.p.m., (e) 257 r.p.m. 

263. An engine drives a band wheel 6' in diameter at 
175 r.p.m. What is the diameter of the pulley on the dyna¬ 
mo running at 900 r.p.m.? 

264. A type “R” motor runs at 1274 r.p.m. With a 15 
tooth pinion, what will be the number of teeth in the gear 
when connected to a machine for 182 r.p.m.? 

265. If gears of 5 diametral pitch are used in problem 
No. 264, what is the distance between gear centers? 

266. An Air Compressor in D-3 runs at 167 r.p.m. What 
is the gear ratio when driven by an 875 r.p.m. motor? 

267. The compressor in problem No. 266 has a gear of 
68 teeth; how many teeth has the pinion on the motor? 

268. A double belt will transmit 1 3/7 times as much 
power as a single belt of the same width. If a 6" single belt 
will transmit 11.8 h.p., what h.p. may be transmitted by a 
6" double belt? 

DENSITY AND SPECIFIC GRAVITY. 

Density is weight per unit volume. Any units may be 
used; the most common units are pounds per cu. ft. and 
grams per cubic centimeter. Thus: the density of water is 
62.5 lbs. per cu. ft. or 1 gram per cubic centimeter. 

The density of different substances may be compared. 
Such comparisons give rise to the use of relative density or 
specific gravity. 

Specific gravity is the density of a substance expressed 
in terms of the density of some other substances as a base. 
Therefore the specific gravity of water is 1. Since the 
density of water is 1 gram per cubic centimeter, the specific 
gravity of any substance is equal to its gram weight per 
cubic centimeter. 

The specific gravity of a substance is an abstract quantity, 
because it is the ratio of two weights. 

To find the specific gravity of a substance, divide the 
weight in pounds of one cubic foot of the substance by the 
weight of one cubic foot of water. 


38 


The weight of a body when given in grams per cubic 
centimeter is the same as its specific gravity. Example? 
If a cubic centimeter of metal weighs 8.5 grams, the specific 
gravity of that metal is 8.5. 

The specific gravity of water is 1; Cast brass, 8.1; Bronze, 
8.5; Anthracite coal, 1.5, and Bituminous coal, 1.32. There¬ 
fore as 1 cu. ft. of water weighs 62.5 lbs., 1 cu. ft. of cast 
brass would weigh 8.1 x 62.5 lbs., or 506.25 lbs., and 1 cu. ft. 
of bronze would weigh 8.5x62.5 lbs., or 531.25 lbs. etc. 

269. Find the number of cubic feet in 1 ton of water. 

270. What is the weight of 1,000 feet of aluminum wire 
in diameter? 

271. Find the number of lbs. of cast brass necessary to 
put a %" lining in a bearing 4%" in diameter and 10" 
long. 

272. What is the thickness of a square bar of bronze that 
is 18" long and weighs 30 lbs.? 

273. What will be the weight of a box 4' long, 2' 4" wide 
and 16" deep, made from %" cherry wood? 

274. What will be the width of a 5' vein of anthracite 
coal to produce 1% tons per foot? 

275. What will be the width of a 5' vein of bituminous 
coal to produce IV 2 tons per foot? 

276. What will be the thickness of a sheet of cork that 
is 2' square and weighs 15.6 lbs.? What is its specific 
gravity ? 

277. What is the weight of 1,000' of elm wood? What 
is its specific gravity? 

278. What is the thickness of a plate glass window 9' 
by 12' that weighs 583.2 lbs.? 

279. What is the specific gravity of gold? 

280. What is the weight of a bar of gold 8" by 4" by 2" ? 

281. What is the volume of enough cast-iron to load a 
60,000 lb. freight car? 

282. What is the weight of a hickory rod 3' long and 
1*4" in diameter? 

283. What is the weight of a fuse block 9%" by 3 V 2 " 
by 21 / 4 " made from lignum-vitae? 

284. What is the specific gravity of lead? 

285. How many shot each 3/16" in diameter can be 
made from 100 lbs. of lead? 


39 

286. How many sheets of mica each 2' square by 1/16" 
thick will be required to weigh 50 lbs.? 

287. What will be the weight of the mercury in a vessel 
2 " in diameter and 6" high? 

288. What is the specific gravity of mercury? 

289. What is the length of 1 lb. of platinum wire .01" 
in diameter? 

290. What is the volume of an 80 lb. steel rail 30' long? 

291. The specific gravity of zinc is 7.0. Find its weight 
per cubic inch. 

292. A block of ice 2' thick, floats with 1".92 above 
water. Find its specific gravity. 

293. One thousand feet of southern pine board weighs 
1.674 tons. Find its volume and specific gravity. 

294. The specific gravity of sulphur is 2. What are the 
dimensions of a cube weighing 62% lbs.? 

295. How much peat can be stored in a space that will 
hold 5 tons of bituminous coal? 

296. What is the weight of a brick of silver 8" by 6" by 
4". Specific gravity of silver is 10.5. 

297. The specific gravity of marble is 2.7. What is the 
weight of a block containing 25 cu. ft.? 

298. How many bushings each 2" long, 1 / 4" thick, %" 
outside diameter, can be made from 100 lbs. of hard rubber? 

299. A body weighs 10 lbs. in air, 5 lbs. in water, and 
5.83 lbs. in alcohol. Find the specific gravity of alcohol. 

300. A cubic inch of aluminum is 2.67 times heavier 
than a cubic inch of water, and a cubic inch of cast-iron is 
7.218 times heavier than a cubic inch of water. If a pat¬ 
tern made of cast-iron weighs 35 lbs., what would it weigh 
if made of aluminum? 

301. Calculate the specific gravity of sea water from the 
following data: 

Weight of bottle, empty_3.5305 g 

“ “ “ filled with water_7.6722 g 

“ “ “ “ “ sea water_7.7849 g 



40 


ALLOYS AND MIXTURES. 

An alloy is a mixture of two or more metals to form a 
new compound, such as steel, bronze or brass. A mixture 
is the same as an alloy, but is usually referred to when 
speaking of liquids, as: a mixture of water and sulphuric 
acid. 

302. A quantity of brass is made up of 70.2% copper 
and 29.8% zinc. If it contains 12 lbs. of zinc, how much 
copper was used? What is the total weight of the brass? 

303. Using the same proportion as in problem No. 302, 
how many pounds of each metal in a quantity of brass 
weighing 142 ibs.? 

304. Referring to problem No. 302. A quantity of brass 
contains 57 lbs. of copper, what is the entire weight of the 
alloy? How many lbs. of zinc does it contain? 

305. A certain alloy contains 13.3 oz. of gold—what is 
the entire weight of the alloy and how much of each metal 
was used if the alloy is composed of 66.5 parts gold, 15.4 
parts copper, and 18.1 parts silver? 

306. If an alloy contains 5 parts zinc, 2 parts tin and 1 
part lead, how many pounds of each metal are used, sup¬ 
posing there were 40 lbs. of tin in the alloy? 

307. A German silver alloy contains metals in the fol¬ 
lowing proportions: Copper, 60.16%; zinc, 25.37%; nickel, 
14.03%; iron, .3%; the remainder is equal parts of cobalt and 
manganese. A quantity of this alloy contains 1 oz. each of 
cobalt and manganese. How much of each of the other 
metals does it contains? What is the total weight of the 
alloy? 

308. Manganin is an alloy of copper, manganese and 
nickel. A quantity of the alloy contains 2.28 lbs. of nickel, 
684 lbs. of manganese and 47.88 lbs. of copper. What is 
the weight of the whole quantity of alloy? What percent¬ 
age of each metal does the alloy contain? 

309. How many pounds of each material will be neces¬ 
sary to make one mile of 100 lbs. steel rails? Carbon, .45%; 
phosphorus, .10%; silicon, .20%; manganese, .84%; bal¬ 
ance iron. 

310. Manganese-copper contains 2 y 3 times as much 
copper as manganese. What is the percentage of each 
metal in the alloy? 


41 

311. A solution for cleaning copper is made of 100 parts 
water, 100 parts sulphuric acid, 50 parts nitric acid, 2 parts 
hydrochloric acid. How much of each liquid will be re¬ 
quired to make 5 gallons of the solution? 

312. A solution for cleaning iron is made of 25 parts 
each of hydrochloric and nitric acid, 10 parts sulphuric 
acid and 1,000 parts water. How many gallons of solution 
will contain % pint of nitric acid? How much of each of 
the other liquids in this solution? 


RAILROAD CONSTRUCTION. 


313. How many 30' rails will be required to lay 1 mile 
of single track? 

How many 30' rails will be required for five miles 
of double track? 

314. With rails weighing 70 lbs. per yard, how many 
tons of steel will be required for 35 miles of single track? 

315. With 100 lb. rails, how much steel will be required 
for 18 miles of double track? 

At $36.75 per ton, find cost of 100 lb. rails for six 
miles of double track. 

316. Allowing 1500' for a switch track every 5 miles, 
how much steel must be provided for turn-outs in problem 
No. 315? 

317. With one 250' cross-over every three miles, find 
how much steel will be required for cross-over in problem 
No. 314? 

318. With two fish plates per rail joint, find the number 
required for 2 miles of single track. 

319. Using four bolts through each fish plate at rail 
joints, find the number of bolts required for 3 miles of 
single track. With six bolts per joint, find the number of 
bolts required for 2 miles of double track. 

320. Allowing 12 ties per rail length, how many ties will 
be required for 3 miles of single track? 

What is the total number of ties required for 35 
miles of double track? 


42 


321. With two spikes per rail in each tie, find the num¬ 
ber of spikes required for 10 miles of single track. 

Allowing 5% additional for guard rails on curves 
and trestles, find the amount of steel and the number of 
fish plates, bolts and spikes required for 5 miles of double 
track. 

322. A 5%" square spike weighs 3/7 of a lb., how many 
spikes are in a 150 lb. keg? 

How many kegs of spikes are required for 5 miles 
of single track? 

323. How many pounds of %" bolts are required for 
32 miles of single track? (100 bolts, equal 78 lbs.) 6 bolts 
per rail joint. 

324. What will %" bolts cost at $4.50 per 100 lbs. for 3 
miles of double track? 

What will be the cost of spikes at $3.10 per 100 lbs. 
for 4 miles of double track? 

325. At 45 cents each, what will the fish plates cost for 
18 miles of single track? 

At 50 cents each, what 
will be the cost of ties for 
12 V 2 miles of double track? 

326. The attached sketch 

shows a section of railroad 
bed and track. How many 
cubic yards of ballast will 
be needed for 1 mile of 
track? “A” or top of road¬ 
bed is 10', “B” or base of 
road-bed is 12'; “C” is 1', 
the depth of ballast. The 
ties are long by 9" by 
6 " and are embedded in the 
ballast. Twelve ties are 
used per rail length. 1*--b- ] 



327. At $1.25 per cu. yd., what will be the cost of ballast 
in problem No. 326? 
























































43 

328. At $700.00 per mile of single track, what will it 
cost to lay 37 miles of double track? 

329. This shows a cross-section 
of a hill and represents a cut to be 
made for a road-bed. The slope of 
the hill is IV 2 to 1. What is the 
depth of the cut “A” if “B” is 9' ? 

How many cubic yards of material must be removed if 
the cut is 90' long? 

330. “C.D.” represents the cross- 
section of a cut 175' long. “D” is 
18' wide; “C” is 7' deep. What is 
the width of cut at top if the slope 
is 1 to 1? 

How many cubic yards of material must be removed? 

331. “E.F.” is a till with a slope 

of 1i/4 to 1. “F,” the top of the 

road-bed, is 18' wide. How many 
cubic yards of material will be 
needed to make a fill 137 yds. long? 

“E” is 12' high? At 23.5 cents per 
cost to make the fill? 

332. The length of this fill is 
257 yds. The height of fill is 9', 
with a road-bed 18' wide; if the 
slope is 1% to 1, what quantity of 
material is needed? 



cubic yard, what will it 





*333. A contractor agreed to build an embankment for 
a railroad up a slight incline plane, the bed for the track to 
be level. The embankment to be 400' long and the width of 
the bed for the ties 12' wide; the perpendicular measure- 
• ment of the higher end was to be 20' and at the lower end 
16'; the width of the embankment at the higher end at the 
bottom was to be 36', and at the lower end 24'. What was 
the cost at 23.5 cents per cubic yard? Draw sketch. 




















44 


Westinghouse Electric & Manufacturing Company’s 
Standard List of Forged Cutting Tools. 


LATHE. PLANER AND SHAPER 
TOOLS. 

1. Straight threading. 

2. R. H. bent threading. 

2%. Shoulder Threading. 

3. Left side cutting off. 

4. Radius. 

{>. Straight cutting off. 

6. 45° left cutting off—bent. 

7. 45° right cutting off—bent. 

8. Inside finishing—boring. 

9. Diamond point—boring. 

10. Round nose—boring. 

11. Inside threading. 

12. Inside square threading or fin¬ 
ishing. 

13. R. H. side. 

14. L. H. side. 

15. 45° L. H. cutting edge. 

16. 45° R. H. cutting edge. 

17. L. H. inside bent facing, R. H. 
cutting edge. 

18. R. H. inside bent facing, L. H. 
cutting edge. 

19. R. H. round nose turning and 
planing. 

20. L. H. round nose turning and 
planing. 

21. R. H. diamond point lathe. 

22. L. H. diamond point lathe. 

25. Brass turning. 

26. L. H. bent roughing, L. H. cut¬ 
ting edge. 

27. R. H. bent roughing, R. H. cut¬ 
ting edge. 

28. Straight tapering brass turning. 

29. Straight brass, long tapering. 

31. 30° L. II. brass turning. 

31 %. 15° L. H. brass turning. 

32. 30° R. H. brass turning. 

32%. 15° R. H. brass turning. 

34. 30° Left wide nose bevel turn¬ 
ing and finishing. 

35. 30° Right wide nose bevel 
turning and finishing. 

36. Round nose hooked, copper 
turning. 

37. Copper turning. 

38. L. H. diamond point planer. 

39. R. H. diamond point planer. 

40. R. H. shaft roughing. 

41. L. H. shaft roughing. 

43. Left bent copper turning. 

44. Right bent copper turning 
47. Centering. 

50. R. H. roughing, side facing. 

94. Left bent 90° cutting off. 

95. Right bent 90° cutting off. 

96. Finishing or square nose. 

100. R. H. finishing or shear nose. 

101. L. H. finishing or shear nose. 

102. Goose neck planer. 

103. Left bent diamond point, L. H. 
cutting edge. 

104. Right bent diamond point, R. H. 
cutting edge. 


BORING MILL TOOLS. 

106. Right round nose roughing. 

107. Left round nose roughing. 

122. Straight cutting off. 

123. Left compound brass. 

124. Right compound brass. 

125. Left side. 

126. Right side. 

127. Right bent square nose rough¬ 
ing. 

128. Left bent square nose roughing. 

129. Inside boring, diamond point. 

130. Facing or finishing. 

131. Left side, cutting off. 

132. Right side, cutting off. 

133. Circle cutting off grooving. 

134. 90° Left cutting off grooving. 

135. 90° Right cutting off grooving. 

136. Left clear nose roughing. 

137. Right clear nose roughing. 

138. R. H. and L. H. facing. 

139. Double facing. 

140. L. H. off set facing. 

177. Left boring. 

178. Right boring. 

SLOTTER TOOLS. 

150, 150%, 151. Roughing. 

151%, 153, 153%, 154, 154%, 155, 156, 
157, 157%, 158. Key way. 

163. Diamond point. 

163%. Square point. 

FOX LATHE TOOLS. 

183. 90° Left cutting off. 

184. 90° Right cutting off. 

185. L. II. turning. 

186. R. H. turning. 

187. Brass. 

189. Left inside threading. 

190. Right inside threading. 

191. L. H. round shank boring. 

192. R. H. turret boring. 

193. 90° L. H. round shank cutting 
off. 

194. 90° R. H. round shank cutting 
off. 


J. & L. LATHE. 

1, 2. Roughing. 

3. 1" Inside facing and recessing. 

4. %" Inside facing and recessing. 

5. Boring. 

6. Roughing. 

7. Finishing or square nose. 

8. Outside facing, turning and 
recessing. 

9. Side left hand. 

10. Side right hand. 

11, 12. Boring bar same as 9 & 10. 

13. Left facing and chamfering. 

14. Right facing and chamfering. 

15. Right side. 




WESTINGHOUSE ELECTRIC & MANUFACTURING COMPANY 

FORGED CUTTING TOOLS. 


44 A 


Wm 















45 


THINGS TO BE REMEMBERED WITH REGARD 

TO CUTTING TOOLS 

The cutting action of the tool tends to compress the 
metal which is being cut, and as the power recpiired to 
drive the work against the tool is in direct ratio to the 
correctness or incorrectness of the cutting angles and rake, 
it must be apparent that any change in these angles means 
power gained or lost, which in turn means a larger or a 
smaller coal consumption, and this is money. The ques¬ 
tion that is agitating the manufacturer and has been the 
problem for the past few years, is a scientific method of 
caring for these cutting edges. Remember that the cutting 
tool is the basis of economic production, and the more 
scientific method we have of maintaining these proper cut¬ 
ting angles, the more economic is their use. 

The old feeling that was so prevalent in the minds of 
many executives and to some extent exists today, namely, 
that no two mechanics grind a tool alike, and that any 
suggested change would hurt the workman’s feelings, was 
a vital one. This attitude worked against any progressive 
system up to within four or five years ago. 

It is now conceded that all tools should be ground in a 
central tool room, by a set of experienced men who know 
and appreciate the importance of correct angles. 

Few men know Tool Steel, hence, they do not abuse it 
intentionally but through ignorance. 

Tool Steel has character just as the human being 
has character and it needs the same handling to produce 
the highest efficiency. 

Steel can readily be burnt on an . abrasive wheel and 
the operator not be cognizant of it. 

All this the experienced men know and in consequence 
use light pressures against the wheel, with a plentiful supply 
of water. 

Don’t grind on a dry stone and then dip in water, if 
you wish to use the tool, because the change from expan¬ 
sion to contraction is too abrupt. 

Keep in mind that tools should be kept sharp; the same 
angles should be maintained, and when necessary for the 
operator to grind his own tools, he should see that very 
little heat is generated, between the tool and the stone, by 
undue pressure. Always grind the tools wet. 


46 


THE LEVER. 


Levers are of three classes—First, second and third. The 
product of the force by the power-arm is equal to the prod¬ 
uct of the load by the load-arm. Then: force times power- 
arm equals load times load-arm, or— 

Wa Pb Wa Pb 

Pb=Wa, or P=—. or W=—> or b=— or a=— 

b a P W 


W—Weight or load. 
P —Force. 

F —Fulcrum. 


a—Load-arm. 
b—Power-arm. 


In the first-class the fulcrum 
is between the load and the 
force. 

In the second-class the load 
is between the fulcrum and the 
force. 

In the third-class the force is 
between the fulcrum and the 
load. 

The first-class is illustrated by 
a spade, second-class by a pinch- 
bar, third-class by the forearm. 
How many other things can you 
mention that will illustrate any 
of the three cases? 



F 

2nd Class 


p 



F 


3rd Class 


Given 

P b W a Find 


334. 

335. 

336. 

337. 

338. 

339. 

340. 

341. 

342. 

343. 


_10 ft_100 lbs_1 ft_P 

_2 yds._3 cwt. 15 lbs_1 ft. 6 in.—P 

200 lbs._1 ton_8 in_b 

1524 lbs_29 lbs_5 ft. 11 in._b 

56 lbs_43 in_4 ft. 1 in.__W 

900 lbs_1 yd. 7 in_1 ft. 2 in.__W 

39.5 oz_1 yd. 2 ft..12 lbs_a 

16 tons_5 in._1250 lbs_a 

_14 ft_140 lbs_14 in_P 

21.67 lbs._31.7 in_49.3 in_W 









































APPARATUS USING PRINCIPLE OF LEVER. 


47 


Balances:—Load-arm equals 
power-arm. Class 1. 

Therefore load and force are 
equal. A lever of 1 to 1 ratio. 

344. What weight in P will 
balance 12 lbs. in the scalepan 
W? 

Steelyard, Class I. Load-arm 
shorter than power-arm. Length 
of load-arm is constant. Force is 
constant. Length of power-arm 
is variable. Therefore, the steel¬ 
yard may be used to measure 
loads of different weights. 


F 




345. The load-arm of a steel¬ 
yard is 2" long. The power-arm is 
one yard long and has a 5 lb. bal¬ 
ance weight. Where must the 
weight be placed to balance a load 
of 50 lbs.? The power-arm is 
marked in quarter inches. 


346. A certain steelyard has a load-arm 1".5 long and 
the power-arm is 2' 6" long. What must be the weight at 
end of P to balance a load of 50 lbs.? 


347. If P weighs % lb., and the load-arm is 2" long, 
find the position of P on the power-arm to balance a load 
of 3 lbs., 8 lbs., 10 lbs., 293 oz. 

348. The lever principle is used in the Wheel and Axle, 
the Windlass and in the Capstan. In each case the fulcrum 
is at the center of the axle. The length of the load-arm 
equals the radius of the axle plus the radius of the rope or 
cable. The power-arm is the crank-arm. In the attached 
sketch the crank-arm is 2' long. The axle is 5" in diameter. 
A 1" rope is used. What weight 
can be lifted by a force of 10 lbs.? 

349. The crank of a Windlass 
is 26" long. The diameter of the 
axle is 6" long and a 1".5 cable is p 
used. What force will be required 
to lift 1 ton? 













































48 

350. The bell-crank is a form of lever used to change 
the direction of a force. It may also change the amount of 
force. To change the direction only of the force the arms 
are of the same length. To change the amount of force, the 
arms are of different lengths. 

In the sketch, A is 16" long, B is 
2" long. What weight can be 
moved at end of B with a force of 
15 lbs. at the end of A? 

351. The arms of a bell-crank 
are at right angles. The load-arm 
is 4" long and the power-arm is 
10" long. How much vertical pull at P will produce a 
horizontal pull of 60 lbs. at W? 

352. If a force of 10 lbs. is to balance a weight of 40 lbs., 
what is the ratio of the lever arms? 

353. If the ratio of the power-arm to the load-arm is as 
3 to 7, what weight may be lifted by a force of 58 lbs.? 

354. In problem No. 353, what force will lift a weight 
of 116.8 lbs.? 

355. What must be the ratio of the lever-arms if a load 
of 280 lbs. is handled by a force of 56 lbs.? 

356. If the ratio of the load-arm to the power-arm is as 
9 to 4, what load may be lifted by a force of 36 lbs.? 

357. If the power-arm is l 1 ^" long and the load-arm is 
12 %" long, what is the ratio of the weight to the force? 

358. A lever 54" long, has a weight of 20 lbs. on one end 
with the fulcrum 6" from the end nearest the weight. Find 
what force must he exerted to raise it from the ground? 

359. A lever A. B. 8' long is supported at A. A weight 
of 40 lbs. is hung at C, 3' from A. What power at B will 
balance it, and what is the pressure on the fulcrum? 

360. In a lever A. B. 8' long, the fulcrum C is 10" from 
B. What weight is required at B to balance 10 lbs. at A? 

361. A lever 54" long has the fulcrum at one end and a 
20 lb. weight at the other end. Find what force at 6" from 
the fulucrum will lift the weight? 

362. If the radius of a wheel is 3and the radius of 
the axle 5", what force at the rim of the wheel will be re¬ 
quired to balance a resistance of one ton at the radius of 
the axle? 












49 


363. A weight of 25 lbs. balances 212 lbs. and the radius 
of the wheel is 28". Find the radius of the axle. 

364. The power-arm of a lever is 10' long. The load- 
arm is 5' long. How long will the lever be if it is of the 
first class? How much weight can be lifted with a force 
of 50 lbs.? 

365. If the length of the power-arm is constant, what is 
the length of the lever and weight lifted, if the lever is of the 
third class? See problem No. 364. 

366. If the position of the fulcrum and the power are 
interchanged, what is the length of the lever and weight 
lifted, if the lever is of the second class? See problem 
No. 364. 

THE PUMP. The suction pump 
consists of a cylinder or barrel, a 
piston, two valves and a suction 
pipe, the lower end of which dips 
below the surface of the water. The 
piston works practically air tight 
in the cylinder and has an outlet 
valve that opens upward. The inlet 
valve is at the upper end of the sue- ® 
tion pipe and also opens upward. 

The practical limit for a pump lift¬ 
ing water by suction is 28 vertical 
feet. Theoretically this distance is 
32 feet. Consult some books on 
Physics for a further explanation. 

367. How many gallons of water 
will a force of 2 lbs. raise at each 
stroke of the pump handle? The 
horizontal distance from F to W 
is 4", and horizontal distance from F to P is 2'. 

368. The piston in No. 367 is 3" in diameter and has a 
6 " stroke. What amount of water will be lifted at one full 
stroke? 

369. Under the conditions of problem No. 368 and mak¬ 
ing 40 strokes per minute, how long will it take to pump 15 
barrels of water? 

































50 


The safety valve on a steam engine represents what class 
of lever? What is the use of the safety valve? Are all 
safety valves made with an arm carrying a weight to regu¬ 
late the steam pressure? Do all 
steam boilers carry the same 
amount of steam pressure per 
square inch ? What would happen 
if the safety valve failed to oper¬ 
ate? Bring in a sketch of a safety 
valve of a different type. 



370. If a 50 lb. weight is used and the diameter of escape 
valve is 2", where must the weight be placed so that the 
steam will blow off at 90 lbs. pressure? The length of the 
power-arm is 3". 


MACHINE SHOP. 

371. A straight shaft 1%" in diameter and 30" long is 
to be turned from 2" stock. How many cubic inches of 
metal must be removed? How many pounds of metal 
must be removed? 

372. If the lathe in problem No. 371 makes two rough¬ 
ing cuts 15/64" in depth, on diameter, what will be the per¬ 
centage of the total metal to be removed which is taken off 
by the roughing cuts. How many cubic inches? How 
many pounds? 

373. In problem No. 371, how much is taken off by the 
third or finishing cut which leaves the shaft 1".51 in. 
diameter? 

374. After the finishing cut, the shaft is ground to size. 
How much metal is removed by the grinder? See problem 
No. 371. 

375. In problem No. 371 the lathe makes 160 r.p.m. 
What is the linear cutting speed at the surface of the stock? 

376. In problem No. 371, with 1/32" feed, how long will 
it take to make each cut? 

377. A car axle of the dimensions given below is to be 
turned from b 1 /^" straight stock of axle steel. Find the 
total length of the axle. The dimensions are A, B, 8"; 
C, 2"; D, 71 / 2 "; E, 6"; F, 3' 6%"; G, 7y 2 "; H, 2"; K, 8"; 
L, M, 51/4"; N, 41/4"; 0, 51/4"; P, 53 / 4 "; Q, 6"; R, 5 y 2 "; 
S, 5%"; T, 5%"; U, 4%"; V, 5*4". Find the weight of 
the rough stock. 







51 


378. Find the weight of finished axle 
in problem No. 377. 

379. What would be the diameter 
of a straight shaft of the same weight 
and length as in problem No. 377? 

380. How much steel was turned off 
in making the axle in problem No. 377? 

381. What percentage of weight is 
lost in turning the axle in problem No. 
377? 

382. If the steel is removed at the 
rate of 96 lbs. per hour, how long will 
it take to machine the axle? See prob¬ 
lem No. 377. 

383. A planer hand has a job that 
he can complete in 12 hours. Suppose 
the efficiency of the machine would be 
reduced by accident when the job is 
% finished. How long will it be neces¬ 
sary for him to work at that rate in 

order to finish the job? 

• 

384. If it is estimated that a man 
will do 40% more work in a given time 
than a boy, will 36 men do a given 
amount of work quicker than 50 boys? 

385. An automatically fed punch 
press will turn out 270 punchings in 1 
minute. By an ordinary hand fed punch 
press these punchings were made at the 
rate of 105 per minute. What per cent, 
of labor is made unnecessary by the au¬ 
tomatically fed press if one man can at¬ 
tend four such presses? 

386. The efficiency of a planer has 
been reduced *4 by long and hard use. 
If a workman begins a job of machining 
12 spiders on a new machine and is 
given the old machine to finish the work 
when he is half done, how long will it 
take him? On the new machine he fin¬ 
ished a spider in 2 hours. 


1 


1 

L 1 


i 


—*- 

► 

► 

» 


* M * 

K 

}> 



V 


— /V 

— 

t 

1 , 

ry 



t 


q h „ 



c 





£ 

3 


* wL* * 


t~L—s—3 


Journal. Wheel Seat. Gear Seat. Wheel Seat. Journal. 



















































52 


387. Of the 30 machines sent to the testing department 
on Monday, 27 were delivered for shipment and three were 
returned to the assembling department for repairs. There 
were four men on the test, each rated at 20 cents an hour. 
What was the average cost of testing per finished machine, 
and what was the average time required per finished ma¬ 
chine? 

388. A man sets up a piece of work and drills 800, V 2 " 
holes per day’s work. By the use of the Gang Drill he is 
able to drill 2400 holes in the same amount of time. What 
decrease per cent, in manual labor required is here effected 
by the use of the Gang Drill? 

389. How many men would be required to drill 96000 
per week by old method? See problem No. 388. 

390. How many men would be required to drill 96000 
per week by new method? See problem No. 388. 

391. It is estimated that 160 J. & L. machines will pro¬ 
duce as much work as can be done on 500 ordinary turret 
lathes working the same number of hours. What per cent, 
of labor have these machines displaced? 

392. By an ordinary hand-fed punch press a certain 
punching can be made at the rate of 70 per minute. With 
an automatically fed press 180 of the same punchings can 
be made. What per cent, of labor is made unnecessary by 
the automatic feed if one man can attend four such presses? 

393. A planer hand has a piece of work which is esti¬ 
mated will require 10 hours 30 minutes to finish. Suppose 
the efficiency of the machine would be reduced by acci¬ 
dent when the job is finished. How long will it be neces¬ 
sary for him to work at that rate in order to finish the job? 

394. A lathe used in turning shafts, operating with ordi¬ 
nary commercial tool steel, runs at a speed of 220 r.p. 111 . 
By introducing tools made of high speed steel, the rate of 
cutting was increased 30%. At what speed could the lathe 
be operated? The shafts being roughed out by this lathe 
were 4" in diameter. 

395. Two lathes are driven from the same counter-shaft 
and from the same size pulleys on the counter-shaft. The 
first lathe that is running at 240 r.p.m., the diameter of 
pulley is 5". What will be the speed of the second lathe if 
the diameter of its pulley is 20% greater than the pulley on 
first lathe? 


53 

396. A piece of steel sent to the chemical laboratory 
shows the following analysis: Phosphorous, .04%; manga¬ 
nese, .60%; sulphur, .035%; carbon, 2.5%, and the balance 
pure iron. How many pounds of each metal in a casting 
that weighs 2 tons? 

397. A sample piece of steel upon analysis shows the 
following: Sulphur, .045%; manganese, .715%; phosphor¬ 
ous, .045%; silicon, .265%; carbon, .55%. What is the 
actual weight of each substance in 500 lbs. of this grade 
of steel? 

398. A “T”-shaped casting is represented by a drawing, 
on which the scale used is 3" to a foot. The top part meas¬ 
ures 5" and the upright part measures 7". Both are %" 
wide and %" thick. What will be the dimensions of the 
pattern? No allowance to be made for shrinkage. 

399. It is desired to make 50 castings from the pattern 
referred to in the above problem. They are to be made of 
brass, the alloy to consist of 16 lbs. of copper to 9 lbs. of 
zinc. How many pounds of each metal are required? Make 
a total allowance of 15 lbs. for the loss in casting and fin¬ 
ishing. A cubic foot of this alloy weighs 523.2 lbs. 

400. We have a ton of bar iron, each bar weighing 80 lbs. 
Two-fiftlis of this iron is cut up for shafts, % of what re¬ 
mains is used for bolts, and the balance is made into studs. 
How many bars are used for the different articles? 

401. How much iron is used in the building of an arma¬ 
ture 22" long, if the punchings are ".0625 thick? What is 
the weight of the armature when finished, if each punching 
weighs 7 oz., the commutator 75% lbs., the wire used in 
winding 7% lbs., and the shaft 90% lbs.? 

402. A sample of steel used on gear tires upon analysis 
showed the following: Carbon, .6%; silicon, .27%; phos¬ 
phorous, .045%; manganese, .72%; sulphur, .047%, and the 
balance in iron. If the tire weighs 360 lbs., what is the 
actual weight of each substance in this tire? 

403. What is the maximum speed allowable to drive a 
cast iron pulley 48" in diameter if 5,000' per minute is the 
safe allowable peripheral speed for cast iron? 

404. We have set up on a vertical boring mill an induc¬ 
tion motor frame, the finished inside diameter of which is 
to be 18". What is the rate of machining the metal on 
finishing cut if mill is running at 200 r.p.m.? 


54 


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ENGINE LATHE. 

The I„odge & Shipley Machine Tool Company - Cincinnati, Ohio 



































JH 





55 


THE LATHE. 

The lathe is the most important machine used for manu¬ 
facturing purposes because it embodies nearly all the prin¬ 
ciples of the other machines. 

What is a lathe? Draw a rough sketch of a lathe and 
name the principal parts. What determines the size of a 
lathe? Name the make of lathe on which you are working 
or have worked. What is the effect of offsetting the tail- 
stock? Lathes are also used for turning tapers on round 
stock. A common method for setting the lathe for turning 
tapers is to off-set the tailstock center so that it is out of line 
with the driving center. When the taper is to be turned the 
whole length of the bar, the tailstock is off-set one-half the 
difference between the diameters at each end of the piece 
to be tapered. 

404A. The 12" pulley on the counter-shaft of your lathe 
is belted to a 5" pulley on the lathe. When lathe is running 
at a speed of 400 r.p.m., what is the speed of the pulley on 
the counter-shaft? 

405. What is the r.p.m. of the spindle if the counter¬ 
shaft makes 160 r.p.m.? The diameter of the lathe pulley 
is 7%", the diameter of the pulley on the counter-shaft is 

4y 2 ". 

406. A 5" pulley on the counter-shaft makes 175 r.p.m. 
What is the r.p.m. of a lathe cone pulley 814" in diameter? 

407. The taper on a reamer is 8%" long, the small di¬ 
ameter is ".573. The large diameter is ".749. What is 
the taper per foot? 

408. A taper shank on a cutter is 3%" long. The small 
diameter is ".573. The large diameter is ".749. What is 
the taper per foot? 

409. What will be the difference in diameter on a shank 
6%" long if the same taper is used as in problem No. 408? 

410. A bar is turned on a taper for 24" of its length. If 
the large diameter is what must be the taper per foot 
to have the small end 7/16" in diameter? 

411. The difference in the diameters of the ends of a 
taper shank on a cutter is %". What is the length of the 
taper, if the taper is ".600 per foot? 

412. Standard Morse taper is %" to foot. If in a certain 
pinion fit using this taper the bar at large end is 6V2" in 
diameter, what is the size of bar at small end if the length 
of bar is 5^"? 


56 


413. The large diameter of a No. 1 Morse taper spindle 
2%" in length, is ".475. What is the small diameter? Taper 
".600 per foot. 

414. The large diameter of a No. 4 Morse taper spindle 
4-1/16" in length is 1".231. What is the small diameter? 
Taper ".623 per foot. 

415. A taper pin, known as No. 8—4%, has a diameter 
of .492 at the large end of pin. Our standard taper is 1 / 4" 
per foot in diameter. What is the diameter of smaller end 
of this pin? 

416. The small diameter of a No. 2 Morse taper spindle 
2-9/16" in length, is ".556. What is the large diameter? 
Taper ".602 per foot. 

417. The dimensions of a No. 6 Morse taper spindle are 
as follows: Length, 7%", large diameter 2".494, small di¬ 
ameter, 2".077; what is the taper per foot? 

418. A No. 3 Morse taper spindle is ".602 per foot. The 
large diameter of spindle is ".938, the small diameter is 
"759. What is its length? 

What is a thread? What is its use? Explain the differ¬ 
ence between a single and double thread. What is gained 
by using a double or a triple thread? Name the different 
standard threads. Describe each and draw a sketch of same. 
What is meant by pitch? What is meant by lead as applied 
to screws? On what pitches are V threads used? What 
is meant by root diameter? How is root diameter found? 
What is the difference between a V thread, an Acme thread, 
a U. S. Standard thread and a Worm thread? 


What number threads would you cut on the following 
diameters: 1"; 7/16"; 5/16"; %"? 

The root diameter of a V thread is found by dividing 1.732 
by the number of threads per inch, and subtracting this re¬ 
sult from the outside diameter. Also, multiply 1.732 by 
the distance from the center of one thread to the center of 
the next. Subtract this result from the outside diameter of 
the thread. This result is the root diameter. 


419. A piece of work 1 / 4" outside diameter has 20 
threads to the inch. What is the root diameter? What is 
the distance from the center of one thread to the center of 
the next? 

420. What is the root diameter when there are 18 
threads to the inch and outside diameter is 5/16"? 



57 

421. When there are 16 threads to the inch and outside 
diameter is %", what is the root diameter and distance be¬ 
tween centers of adjacent threads? 

422. The outside diameter is 7/16", with 14 threads per 
inch. What is the root diameter and distance between cen¬ 
ters of adjacent threads? 


SCREW AND THREAD CUTTING. 


In order to cut a required number of threads per inch 
on the work in a lathe, the work must revolve, an exact 
number of times, equal to the number of threads to be cut, 
while the carriage which holds the tool moves along the bed 
of the lathe exactly one inch._ The tool is moved by the lead 
screw, which is driven by a set of gears attached to the end 
of the lathe. These gears are driven from the lathe spindle. 
By changing the gears the speed of the lead screw is changed 
so that any number of threads per inch may be cut on the- 
work. Example: If the lead screw is 4 pitch or has 4 
threads to the inch and the work is to have 8 threads per 
inch, then the work must turn twice while the lead screw 
turns once. The set of gears that come with the lathe may 
range from 16 teeth to 84 teeth or more. If the common 
difference between the gears was 4 teeth, the gears would 
be 16, 20, 24, 28, 32, 36, 40 ,44, 48, 52, 56, 60, 64, 68, 72, 
76, 80 and 84. From this set select any two gears, the 
one to have twice the number of teeth of the other; as, 16 
and 32. You would then place the 16 gear on the spindle 
and the 32 gear on the lead screw, because the work which 
is on the spindle must turn twice while the lead screw turns 
once. 

423. A 26" Reed lathe has a lead screw of 4 pitch and 
gears ranging from 20 to 90, with a common difference of 
5, and extra gears 24, 40 and 69. What gears go with this 
lathe? What gears would you use to cut a 12 thread? 

What gears would you use to cut a 16 thread? 

424. A 24" Pond lathe has a lead screw of 2 pitch and 
gears ranging from 16 to 64, with a common difference of 
8 and an extra 66 gear. What gears would you use to cut 
a 6 thread? To cut 8 threads to the inch? 


58 


425. A 16" Reed lathe has a lead screw of 6 pitch and 
gears ranging from 24 to 72, with a common difference of 
4, and an extra 44 gear. What gears do you have? How 
many are there? What ones would you select to cut an 18 
thread? To cut 24 threads to the inch? 

426. A 14" Reed lathe has a lead screw of 8 pitch and 
gears ranging from 24 to 96, with a common difference of 
6 and extra 24, 48 and 69 gears. What gears would you use 
to cut a 20 thread? To cut a 28 thread? 

427. A 24" Pond lathe has a lead screw of 2 pitch and 
gears ranging from 16 to 96, with a common difference of 
8, and an extra 66 gear. What gears would you use to cut 
a 10 thread? To cut 16 threads to the inch? 

428. A 16" Reed lathe has a lead screw of 6 pitch and 
gears ranging from 24 to 72, with a common difference of 
4, and an extra 44 gear. What gears do you have? How 
many are there? What ones would you select to cut a 14 
thread? To cut a 20 thread? 

429. A 14" Reed lathe has a lead screw of 8 pitch and 
gears ranging from 36 to 84, with a common difference of 
6 and extra 24, 48 and 69 gears. What gears would you use 
to cut a 16 thread? To cut a 30 thread? 

430. A 26" Reed lathe has a lead screw of 4 pitch and 
gears ranging from 20 to 65, with a common difference of 

5 and extra gears 24, 40 and 69. What gears would you use 
to cut a 20 thread? To cut a 30 thread? 

431. A 14" Reed lathe has a lead screw of 8 pitch and 
gears ranging from 24 to 96, with a common difference of 

6 and extra 24, 48 and 69 gears. What gears would you 
use to cut a 16 thread? To cut a 40 thread? 

432. What gears would you use to cut a 24 thread on 
the lathe in problem No. 431? To cut an 18 thread? 

433. Using the lathe in problem No. 431 to cut a 32 
thread, what gears would you use? To cut a 10 thread? 

434. A 16" Reed lathe has a lead screw of 6 pitch and 
gears ranging from 24 to 72, with a common difference of 
4. What gears would you use to cut a 20 thread? The ratio 
of the stud to the spindle is 1 to 1. What gears would you 
use to cut a 26 thread? 


59 

435. A 12" P and W lathe has a lead screw of 8 pitch 
and_gears ranging from 28 to 112, with a common difference 
ot 7 and an extra 28 gear. What gears would you use to 
cut a 14 thread? The ratio of the stud to the spindle is 
2 to 1. 

436. What gears would you use to cut a 28 thread on 
the lathe in problem No. 435? 

437. A 26" Reed lathe has a lead screw of 4 pitch and 
gears ranging from 20 to 65, with a common difference of 
5, and extra gears 24, 40 and 69. What gears would you use 
to cut an 18 thread? 

438. What gears would you use to cut a 24 thread on the 
lathe in problem No. 437? 

439. What gears would you use to cut a 36 thread on the 
lathe in problem No. 437? 

440. A 16" Reed lathe has a lead screw of 6 pitch and 
gears ranging from 16 to 104, with a common difference of 
4. What gears would you use to cut a 20 thread? The 
ratio of the stud to the spindle is 1 to 1. To cut a 28 pitch 
thread? To cut a 14 pitch thread? 

UNIVERSAL MILLING MACHINE. 

The universal milling machine is used with various at¬ 
tachments for taking special cuts on work, and more espe¬ 
cially for cutting the teeth of mills, cutters, gears, reamers, 
drills, etc. 

The most important attachment is the index or spiral 
head, which is used with a dead center in tail stock, both 
fastened to a bed or platen that can be moved back or for¬ 
ward in a horizontal plane under a revolving cutter carried 
by the main driving spindle of the machine. 

THE INDEX HEAD. 

The index head is used to divide the periphery of a piece 
of work into any number of equal parts and to hold the 
work at these positions to allow cuts to be taken at equal 
intervals, as in gear cutting, etc. 

The worm wheel of the index head has 40 teeth driven by 
a single thread worm, so that one revolution of the worm, 
which is also the same as one revolution of the index crank, 


60 


No. 4 UNIVERSAL MILLING MACHINE 

Brown & Sharpe Mfg. Co. 
Providence, R. I. 

1. Friction Clutch Levers for starting and stopping Machine. 

2. Power feed lever for longitudinal movement of table. 

3. Power feed lever for transverse movement of saddle. 

4. Power feed lever for vertical movement of knee. 

* i• . t f i v■ "-w . . -,i- 

5. Lever for reversing all powet* feeds. 

• (r«ub ,j 1 .j* nf chi . 

6. Handwheel for quick return of table. 

7. Handwheel for transverse movement of saddle. 

8. Handwheel for vertical movement of knee. 

9 and 10. Knob for disengaging handwheel. 

11. Adjustable dog for controlling length of table movement. 

12. Adjustable dog for controlling length of knee traverse. 

13. Safety dog for preventing table running too far. 

14. Safety dog for preventing knee running too far down. 

15. Spindle drive tumbler gear lever. 

* * 

16. Knob for sliding the tumbler gear. 

17. Quill Gear Lever. 

18. Back dear Lever. 

‘I • j . * ! 

19. Index plate of spindle speeds. 

20. Feed drive tumbler gear lever. 

21. Knob for sliding the tumbler gear. 

22 and 23. Levers for moving change gears. 

24. Lever for clamping overhanging arm. 



NO. 4 UNIVERSAL MILLING MACHINE. 

Brown & Sharpe Mfg. Company - Providence, R. I. 


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61 

will move the spindle carrying the work through 1/40 of a 
revolution; then forty revolutions of crank will give the 
work one complete revolution. If then 40 teeth, or divi¬ 
sions, are required on the work, one revolution of the crank 
will be made between each cut as the work is moved under 
the cutter on the main driving spindle. If 20 teeth, or divi¬ 
sions, are required, the crank will be turned twice around 
for each cut since 20 is one-half of 40, 10 divisions will 
require four turns of the crank; 8 divisions five turns, 5 
divisions eight turns, etc. From this is obtained the for¬ 
mulae for any required number of divisions. 

Let N = number of divisions required. 

R = number of turns of the crank for each cut. 

Then R = 40 -f- N. 

Example: Find the indexing required for cutting a gear 
having 60 teeth. 

40 40 2 

Solution: By Formulae: R=—= — — — ; therefore 

N 60 3 

any plate having the number of holes in a row divisible by 
3 may be used. In this case take the 39 hole index and for 
each one of the 60 teeth cut move the index pin around 26 
holes, since 26 = 2 /$ of 39. 

What is a milling machine? Name some of the principal 
parts of the machine. Is there any class of work that can 
be done on a lathe as well as on a milling machine? What 
is the difference between the work that the lead screw does 
on a lathe and the work the lead screw does on the milling 
machine? 

Name the principal parts of the Index Head on a milling 
machine. Where will you find the spindle on a milling 
machine? What is the worm? How many teeth does it 
usually have? How many threads does the lead screw on a 
milling machine usually have? What is the usual ratio 
between the lead screw and the worm? 

441. Find the indexing for 3 divisions on the work. 

Three plates are used on the index head. The number of 

holes in each plate is, No. 1 equals 15-16-17-18-19-20, No. 2 
equals 21-23-27-29-31-33, No. 3 equals 37-39-41-43-47-49. 

442. If a mill is to have 32 teeth, what is the indexing 
required ? 




62 


443. If a tap is to have 4 flutes, what indexing can be 
used? 

444. What indexing is required to cut 35 teeth on a 
miller? 

445. If you wanted to cut 82 teeth, how would you set 
your index head? 

446. Find the indexing for 68 divisions. 

447. A ratchet wheel is to have 148 teeth. Find the re¬ 
quired indexing. 

448. A circular plate is to be marked on the circumfer¬ 
ence with 164 divisions. What indexing will allow the 
work to be done on the universal miller? 

449. A gear is to have 108 teeth. Find the indexing 
required. 


OHM’S LAWS. 

Pressure = Volts = E F F 

Current = Amperes = 1 E = IR I = — R = — 

Resistance^ Ohms = R R I 

In a hydraulic system the feet head of water is equivalent 
to the volts pressure in an electric system; also, the rate of 
flow or gallons per minute is equivalent to the electrical 
current in amperes; and the friction in the pipes is equiva¬ 
lent to the ohms resistance of the electric circuit. 

450. A current of 21.6 amperes flows in a circuit of 23.1 
ohms resistance. What is the voltage applied to the circuit? 

451. A 95 ohm coil of wire is connected across a 110 
volt circuit. Find the current in the coil. 

452. A generator requires a current through the field 
coils of 150 amps., at 125 volts. What is the field resistance? 

453. An arc lamp takes 6.5 amps, with 42.3 volts across 
the arc. What is the resistance of the arc? 

454. The resistance of 5 lamps in series on a car taking 
current from a 550 volt trolley, is 1100 ohms. What cur¬ 
rent flows in the lamps? 

455. What is the resistance of a car heater which takes 
131/4 amperes at 525 volts? 

456. The candle-power of Incandescent Lamps is pro¬ 
portional to the cube of the voltage of the lamp. If the 
lamps in 454 give 16 c.p. each, what will be the c.p. of each 
lamp when the car passes a sub-station at 600 volts ? 





WEST1NGH0USE DIRECT CURRENT, TYPE “SK” 

COMMUTATING POLE. INDUSTRIAL MOTOR AND PARTS 


62 A 









63 


457. The intensity of illumination varies inversely as the 
square ot the distance from the source of illumination. If 
the c.p. measures 16 at 10', what will be the c.p. at 15'? 

458. When the trolley voltage falls to 300 volts at start¬ 
ing, what is the c.p. per light in 454 and 456? 

459. What must be the resistance of a rheostat to take 
up 9/10 of 220 volts at 7.36 amperes? 

460. At what current would the same rheostate in prob¬ 
lem No. 459 take up 67% of 440 volts? Also 99% of 110 
volts ? 

The Watt is the unit of electrical power. 

1 KW = 1 Kilowatt = 1000 Watts. 

Watts = Volts X Amperes. 

One Horse Power = 746 Watts. 


1 KW= 


1000 

746 


H. P. 


461. What is the h.p. in the circuit of problem No. 460 
if the current delivered is 200 amperes ? 

462. If a motor in circuit of Problem No. 460 requires 
10 h.p. to drive it, what current will it require? 

463. How many watts are taken by a station voltmeter 
that indicates 110 volts and uses a 0.002 ampere current? 

463A. If you have four 40 watt lamps burning 5 hours 
each night for 30 nights, what will be your electric light bill 
if current costs 10 cents per K.W. Hr.? 

464. A group of incandescent lamps absorbs 21 amperes. 
The line loss is 1.5 volts. How many watts are lost? 

465. How many h.p. will be absorbed by a circuit of arc 
lamps, taking 9.6 amperes at 2200 volts pressure? 

466. What mechanical h.p. is necessary for 50 incan¬ 
descent lamps, each taking 0.5 ampere at 110 volts, allow¬ 
ing 10% loss for transformation from mechanical energy 
into electrical energy? 

RESISTANCES. 


R = kX f 

R = Resistance, Ohms. 

K = Constant, dependent upon the material = 

resistant of a mill foot = 10.8 for copper. 
1 = Length, usually in feet. 

a = Area of cross-section, usually in circular mills. 
C.M. = Circular Mills.—C.M. of round wire = di¬ 
ameter in thousandths squared. 



64 


Resistance of a conductor is directly proportional to its 
length and inversely proportional to its cross-sectional area. 

Resistance depends upon material. For Example: Copper 
has low resistance, iron has high resistance. 

467. No. 0000 wire has resistance of 0.26 ohm per mile. 
What is the resistance of 1120' of No. 0000 wire? 

468. No. 0 wire has x /2 the area of No. 0000 wire. What 
is the resistance of No. 0 wire per 1000'? Also, per mile? 

469. The area of No. 0000 wire is 211600 cir. mils. 

The area of No. 000 wire is 167800 cir. mils. 

What is the resistance of No. 000 wire per mile? 

Per 1000'? Per foot? 

470. What is the resistance of 1437' of No. 000 wire in 
series with 3471' of No. 0 wire? 

471. The resistance of No. 10 wire is about 1 ohm per 
1000'. What is the resistance of an induction coil of 2".5 
mean diameter and 3750 turns of No. 10 wire? 

472. The resistance of No. 8 wire is 0.621 ohms per 
1000'. Using No. 467 and No. 469 to get the resistance of 
No. 0000 and No. 000 wire, construct the wire table between 
Nos. 0000 and 12. Each size is double the area of the third 
smaller size. 


The resistance of several circuits in parallel, whose re¬ 
sistances are R 15 R 2 , r 3 , r 4 , etc., is 


R= 


i 

i i 

K I ~~ R 2 



i 

r4 


+ etc, 


the reciprocal of the sum 
of the reciprocals 


The currents in two parallel circuits are inversely propor¬ 
tional to the resistances. 

Resistance of two circuits in series whose resistance in 
Ri & R 2 respectively is Ri + R, 

473. Two circuits of 1.5 ohms and 0.75 ohms are in par¬ 
allel. Find their combined resistance. 


474. A No. 000 trolley is paralelled by a No. 0000 feeder. 
Find the resistance of one mile of trolley and feeder. 

475. Two resistances of 6 ohms and 4.5 ohms are in 
series and are paralleled by a resistance of 10 ohms. Find 
the resistance of the combination. 


476. The combination in No. 475 has 110 volts applied to 
its terminals. Find the total current and the current in each 
branch. 




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65 

477. With 23 volts at the terminals of No. 474, what are 
the currents? 

478. What voltage will send 600 amperes through No. 
473? How will the current divide? 

479. Copper wire increases in resistance .4% for each 
1° Centigrade rise in temperature. A motor field has a re¬ 
sistance of 125 ohms at 20° Centigrade. What will be the re¬ 
sistance at 60° Centigrade? 

A street car is traveling at the rate of 15 miles per hour. 
The diameter of each car wheel is 30". The pinion on the 
motor has 15 teeth and the gear on the axle has 69 teeth 
of 3 diametral pitch. The clearance between gear and 
gear case is 1 / 4". The thickness of gear case wall at the 
bottom is *4". From this data find the following:— 

480. R.P.M. of motor. 

481. Linear speed at pitch line of pinion. 

482. Gear reduction. 

483. Diameters of pitch circles of gear and pinion. 

484. Vertical clearance between gear case and rail. 

485. Distance between gear centers. 

EXPANSION OF METAL DUE TO INCREASE 
IN TEMPERATURE. 

All substances such as gases, liquids and solids undergo 
a change in volume due to an increase in temperature. The 
proof of the following figures does not concern us in this 
work. We will give the following data for the metals most 
frequently used: 


For 1° Fahrenheit. Coefficient of Expansion from 

Metals. 32° to 212°. 

Aluminum (cast) .00001234 .002221 

Copper_.00000887 .001596 

Iron (wrought)_.00000648 .001166 

Iron (cast) 1_.00000556 .001001 

Lead _.00001571 .002828 

Steel (cast)_.00000636 .001144 

Steel (tempered)- .00000689 .001240 


The above figures are for Linear Expansion, or expansion 
in one direction only. For Cubical Expansion multiply the 
linear expansion by three. 






66 


486. A wrought iron bar 22' long is heated from 70° to 
300°. How much will it lengthen? 

Solution: — 22 X (300° — 70°) X .00000648 = '.0327888. 

Coefficients for other materials may he found in any 
standard hand-book. 

487. A round bar of copper 18' long has its temperature 
raised 210°. Find its length after the expansion. 

488. What will be the linear expansion of 1 mile of 
track if the rails were laid when the temperature was 60° 
and is now 95° ? How much space must be left between the 
end of the rails to take care of this expansion? 

489. A bar of cast-iron is found to have increased in 
length '.02376. If the increase of temperature was 240°, 
what was the original length of the bar? 

490. A cube of cast aluminum 2" on an edge is heated 
from 60° to 90°. Find the increased volume. 

491. A steel rail at 70° temperature is 30' long. Find its 
length in winter when the temperature is 5° below zero, 
and also in the summer when the temperature is 98°. 

492. How far apart would you lay the rails in above 
example if you were working when the temperature was 
70°. Range of temperatures from 20° below zero to 100° 
above zero. 

493. A bar of copper has now a length of 22'.03145, 
while originally it was only 22' long. If the temperature 
of bar is 210° at present, what was it at first? 

494. How much will a piece of tempered steel 10" long 
stretch when the temperature is raised from 50° to 90° ? 
From 30° to 70° ? 

495. Find the cubical expansion of a lead ball 3" in 
diameter when the temperature is raised 90° ? 

496. If the cubical expansion of a bar of wrought iron is 
".0983664 and the temperature is raised from 70° to 300°. 
how long is the bar? 

497. How much expansion must be cared for in a struc¬ 
tural steel bridge 1356 feet long if the range in temperature 
is from 25° F. below zero in winter to 110° F. in summer? 
The mean temperature at the time of erecting the bridge 
was 70° F. 


67 

498. What will be the mean diameter of the steel rim of 
an electric locomotive driving wheel at 875° F.? The out¬ 
side diameter of the rim is 62" at 70° F. and thickness of 
same is 4". 

499. The length of Section “R” is 1658 feet. What was 
the expansion to be cared for in erection if there is a range 
of temperature of 40° F. during the } r ear? 

500. The bore of a gear, 8" nominal diameter is bored 
".01 small to allow for shrink fit. This would be specified 
on the drawing thus; bore 8" less ".01. To what tempera¬ 
ture must the bore of the gear be raised in order to apply 
same on the axle or shaft so that sufficient clearance is 
obtained between the bore of the gear and the axle when 
mounting? For this problem consider 1/32" clearance 
radially between bore and axle. 
















































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